Data analytics: handbook of formulas and techniques
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| Format: | Buch |
| Sprache: | English |
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London
CRC Press
2020
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| Schriftenreihe: | Systems innovation book series
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| Beschreibung: | xxv,246 Seiten Diagramme |
| ISBN: | 9780367537418 |
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| 245 | 1 | 0 | |a Data analytics |b handbook of formulas and techniques |c Adedeji B. Badiru |
| 264 | 1 | |a London |b CRC Press |c 2020 | |
| 300 | |a xxv,246 Seiten |b Diagramme | ||
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| 337 | |b n |2 rdamedia | ||
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| adam_text | Contents Preface..................................................................................................................... xxi Acknowledgments.................................................................................................xxiii Author.....................................................................................................................xxv Chapter 1 Essentials of Data Analytics............................................................... I Introduction to COVID-19 Data Analytics.......................................... 1 Systems View of Data Analytics..........................................................2 Global Growth of Data Analytics........................................................2 Background in Predictive Analytics....................................................3 Data Modeling Approaches.................................................................. 5 Data Fanaticism.................................................................................... 6 Data and Measurements for Data Analytics........................................7 What Is Measurement?.................................................................... 7 Data Measurement Systems........................................................ 8 Fundamental Scientific Equations.............................................11 Einstein’s Equation................................................................... 11 Einstein’s Field Equation...........................................................11 Heisenberg’s Uncertainty
Principle.......................................... 12 Schrödinger Equation............................................................... 12 Dirac Equation.......................................................................... 12 Maxwell’s Equations................................................................. 13 Boltzmann’s Equation for Entropy........................................... 13 Planck-Einstein Equation......................................................... 13 Planck’s Blackbody Radiation Formula.................................... 14 Hawking Equation for Black Hole Temperature...................... 14 Navier-Stokes Equation for a Fluid...........................................14 Lagrangian for Quantum Chromodynamics............................ 14 Bardeen-Cooper-Schrieffer Equation for Superconductivity.... 15 Josephson Effect....................................................................... 15 Fermat’s Last Theorem............................................................. 15 Methods for Data Measurement and Comparison......................... 16 Direct Comparison................................................................... 16 Indirect Comparison................................................................. 17 Data Measurement Scales............................................................. 17 Nominal Scale of Measurement................................................18 Ordinal Scale of Measurement................................................. 18 Interval Scale of Measurement................................................. 18
Ratio Scale Measurement......................................................... 18 Reference Units of Measurements................................................. 19 Common Constants.......................................................................20 Numeric Data Representation........................................................20 vii
viii Contents The Language of Data Analytics.......................................................... 21 Quick Reference for Mathematical Equations......................................21 Reference.................................................................................................. 28 Chapter 2 Empirical Model Building......................................................................29 Introduction to the Model Environment................................................ 29 State-Space Modeling.............................................................................30 Calculus Reference for Data Analytics................................................. 32 Integration Rules..................................................................................... 33 Solving Integrals with Variable Substitution.........................................34 Riemann Integral..................................................................................... 34 Integration by Parts.................................................................................34 Compound Functions Where the Inner Function Is ax.................. 34 Integration by Parts........................................................... 35 Systems Modeling for Data Analytics.................................................. 36 Triple C Questions................................................................................... 39 Communication....................................................................................... 40
Cooperation..............................................................................................45 Coordination.............................................................................................47 Conflict Resolution in Data Analytics................................................... 47 References................................................................................................49 Chapter 3 Data Visualization Methods................................................................... 51 Introduction to Data Visualization........................................................51 Case Example of “Covidvisualizer” Website.......................................51 Dynamism and Volatility of Data..........................................................52 Data Determination and Collection..................................................... 53 Choosing the Data............................................................................ 53 Collecting the Data........................................................................... 53 Relevance Check.............................................................................. 54 Limit Check.......................................................................................54 Critical Value.....................................................................................54 Coding the Data................................................................................ 54 Processing the Data..........................................................................54 Control
Total..................................................................................... 54 Consistency Check............................................................................ 55 Scales of Measurement...................................................................... 55 Using the Information....................................................................... 55 Data Exploitation..............................................................................57 Raw Data..................................................................................... 57 Total Revenue..............................................................................58 Average Revenue........................................................................... 59 Median Revenue........................................................................... 61 Quartiles and Percentiles........................................................... 62
Contents IX The Mode................................................................................. 63 Range of Revenue.................................................................... 63 Average Deviation.................................................................... 63 Sample Variance...................................................................... 64 Standard Deviation.................................................................. 65 Chapter 4 Basic Mathematical Calculations for Data Analytics........................69 Introduction to Calculation for Data Analytics..................................69 Quadratic Equation........................................................................... 69 Overall Mean................................................................................ 70 Chebyshev’s Theorem................................................................... 70 Permutations................................................................................. 70 Combinations................................................................................ 70 Failure........................................................................................... 71 Probability Distribution................................................................ 71 Probability.................................................................................... 71 Distribution Function.................................................................... 71 Expected Value............................................................................. 72
Variance........................................................................................ 72 Binomial Distribution................................................................... 73 Poisson Distribution..................................................................... 73 Mean of a Binomial Distribution.................................................. 73 Variance........................................................................................ 73 Normal Distribution..................................................................... 73 Cumulative Distribution Function.................................................73 Population Mean........................................................................... 73 Standard Error of the Mean...........................................................74 f֊Distribution................................................................................ 74 Chi-Squared Distribution..............................................................74 Definition of Set and Notation............................................................74 Set Terms and Symbols..................................................................... 75 Venn Diagrams.................................................................................. 75 Operations on Sets........................................................................ 76 De Morgan’s Laws........................................................................ 76 Probability Terminology............................................................... 77 Basic Probability
Principles......................................................... 77 Random Variable.......................................................................... 77 Mean Value x or Expected Value μ...............................................78 Series Expansions.............................................................................. 78 Mathematical Signs and Symbols......................................................81 Greek Alphabet................................................................................. 83 Algebra...............................................................................................83 Laws of Algebraic Operations.......................................................83 Special Products and Factors.........................................................83 Powers and Roots..........................................................................85
x Contents Proportion............................................................................................ 85 Arithmetic Mean of n Quantities A.................................................. 86 Geometric Mean of n Quantities G...................................................86 Harmonic Mean of n Quantities H................................................... 86 Generalized Mean.............................................................................. 86 Solution of Quadratic Equations.......................................................87 Solution of Cubic Equations.............................................................. 87 Trigonometric Solution of the Cubic Equation................................ 88 Solution of Quadratic Equations...................................................... 89 Partial Fractions.................................................................................89 Non-repeated Linear Factors............................................................ 89 Repeated Linear Factors....................................................................90 General Terms................................................................................... 90 Repeated Linear Factors................................................................... 91 Factors of Higher Degree................................................................. 91 Geometry.................................................................................................91
Triangles.............................................................................................91 Right Triangle.................................................................................... 92 Equilateral Triangle...........................................................................92 General Triangle................................................................................92 Menelaus’s Theorem.................................................................... 93 Ceva’s Theorem........................................................................... 93 Quadrilaterals....................................................................................93 Rectangle...........................................................................................93 Parallelogram................................................................................... 94 Rhombus............................................................................................94 Trapezoid...........................................................................................94 General Quadrilateral...................................................................... 94 Regular Polygon of n Sides Each of Length b................................. 95 Regular Polygon of n Sides Inscribed in a Circle of Radius r...... 95 Regular Polygon of n Sides Circumscribing a Circle of Radius r.,.,95 Cyclic Quadrilateral.......................................................................... 95 Prolemy’s
Theorem............................................................................ 96 Cyclic-Inscriptable Quadrilateral..................................................... 96 Planar Areas by Approximation.......................................................97 Trapezoidal Rule........................................................................... 97 Durand’s Rule............................................................................... 97 Simpson’s Rule (n even)............................................................... 97 Weddle’s Rule (n = 6)...................................................................98 Solids Bounded by Planes.................................................................98 Cube............................................................................................... 98 Rectangular Parallelepiped (or Box)........................................... 98 Prism................................................................................................... 98 Pyramid.............................................................................................. 98 Prismatoid........................................................................................... 99 Regular Polyhedra............................................................................. 99
Contents xi Sphere of Radius r........................................................................... 100 Right Circular Cylinder of Radius r andHeight h......................... 100 Circular Cylinder of Radius r and Slant Height í......................... 100 Cylinder of Cross-Sectional Area A andSlant Height і................ 100 Right Circular Cone of Radius r and Height h............................ 101 Spherical Cap of Radius r and Height h....................................... 101 Frustum of Right Circular Cone of Radii a, b and Height h...... 101 Zone and Segment of Two Bases...................................................101 Lune.................................................................................................101 Spherical Sector..............................................................................101 Spherical Triangle and Polygon.....................................................101 Spheroids.......................................................................................... 102 Ellipsoid....................................................................................... 102 Oblate Spheroid.......................................................................... 102 Prolate Spheroid.......................................................................... 102 Circular Torus............................................................................. 102 Formulas from Plane Analytic Geometry...........................................102 Distance d between Two Points...................................................... 102
Slope m of Line Joining Two Points...............................................103 Equation of Line Joining Two Points.............................................103 Equation of Line in Terms of x Intercept аФ 0 and у intercept Եփ 0...................................................................................................103 Normal Form for Equation of Line................................................ 103 General Equation of Line................................................................103 Distance from Point (x։, yt ) to Line Ax + By + C = 0................... 103 Angle ψ between Two Lines Having Slopes mt and m2............... 103 Area of Triangle with Verticles...................................................... 104 Transformation of Coordinates Involving Pure Translation....... 104 Transformation of Coordinates Involving Pure Rotation.............104 Transformation of Coordinates Involving Translation and Rotation............................................................................................ 104 Polar Coordinates (г, Θ)...................................................................105 Plane Curves..................................................................................... 105 Catenary, Hyperbolic Cosine...........................................................105 Cardioid............................................................................................ 105 Circle.................................................................................................105 Cassinian
Curves..............................................................................105 Cotangent Curve.............................................................................. 106 Cubical Parabola...............................................................................106 Cosecant Curve................................................................................106 Cosine Curve.................................................................................... 106 Ellipse............................................................................................... 106 Gamma Function..............................................................................106 Hyperbolic Functions...................................................................... 106 Inverse Cosine Curve...................................................................... 107 Inverse Sine Curve.......................................................................... 107
XII Contents Inverse Tangent Curve...................................................................... 107 Logarithmic Curve............................................................................107 Parabola.............................................................................................. 107 Cubical Parabola................................................................................ 107 Tangent Curve................................................................................... 107 Ellipsoid..............................................................................................107 Elliptic Cone...................................................................................... 107 Elliptic Cylinder................................................................................107 Hyperboloid of One Sheet................................................................108 Elliptic Paraboloid.............................................................................108 Hyperboloid of Two Sheets............................................................ 108 Hyperbolic Paraboloid.....................................................................108 Sphere................................................................................................108 Distance d between Two Points......................................................108 Equations of Line Joining Ρ։(χ b y,, z։)and P2(x2, yշ, z2) in Standard Form.................................................................................. 108 Equations of Line Joining Vi, Z ) and
P2(x2, y2, z2) in Parametric Form...............................................................................108 Angle j between Two Lines with Direction Cosines A, m,, щ and 1շ,1Ոշ,Ոշ.....................................................................................108 General Equation of a Plane........................................................... 109 Equation of Plane Passing through Points.....................................109 Equation of Plane in Intercept Form............................................. 109 Equations of Line through (x0 Vo · Zo) and Perpendicular to Plane.............................................................................................109 Distance from Point (x, y, z) to Plane Ax + By + D = 0..............109 Normal form for Equation of Plane...............................................109 Transformation of Coordinates Involving Pure Translation....... 110 Transformation of Coordinates Involving Pure Rotation............110 Transformation of Coordinates Involving Translation and Rotation............................................................................................. 110 Cylindrical Coordinates (г, Θ, z)................................................... Ill Spherical Coordinates (г, Θ,........................................................ Ill Logarithmic Identities......................................................................112 Special Values...................................................................................112 Logarithms to General
Base............................................................ 112 Series Expansions............................................................................. 113 Limiting Values................................................................................ 113 Inequalities........................................................................................113 Continued Fractions.......................................................................... 114 Polynomial Approximations............................................................ 114 Fundamental Properties....................................................................115 Definition of General Powers.......................................................... 116 Logarithmic and Exponential Functions........................................ 116 Polynomial Approximations............................................................ 117 Slopes................................................................................................. 125
Contents xiii Trigonometric Ratios.......................................................................125 Sine Law........................................................................................... 127 Cosine Law.......................................................................................127 Algebra.................................................................................................. 127 Expanding.........................................................................................127 Factoring........................................................................................... 127 Roots of Quadratic...........................................................................128 Law of Exponents............................................................................ 128 Logarithms.......................................................................................128 Chapter 5 Statistical Methods for Data Analytics...............................................129 Introduction...........................................................................................129 Discrete Distributions...........................................................................129 Bernoulli Distribution.....................................................................129 Beta Binomial Distribution............................................................ 129 Beta Pascal Distribution..................................................................132 Binomial
Distribution......................................................................132 Discrete Weibul! Distribution......................................................... 132 Geometric Distribution....................................................................132 Hypergeometric Distribution.......................................................... 133 Negative Binomial Distribution...................................................... 133 Poisson Distribution........................................................................134 Rectangular (Discrete Uniform) Distribution............................... 134 Continuous Distributions......................................................................134 Arcsin Distribution.......................................................................... 134 Beta Distribution............................................................................. 135 Cauchy Distribution......................................................................... 135 Chi Distribution............................................................................... 135 Chi-Square Distribution..................................................................135 Erlang Distribution.......................................................................... 136 Exponential Distribution.................................................................136 Extreme-Value Distribution.............................................................136 F Distribution...................................................................................136 Gamma
Distribution........................................................................ 137 Half-Normal Distribution................................................................137 Laplace (Double Exponential) Distribution.................................. 138 Logistic Distribution........................................................................ 138 Lognormal Distribution...................................................................138 Noncentral Chi-Square Distribution..............................................139 Noncentral F Distribution...............................................................139 Noncentral f Distribution.................................................................139 Normal Distribution........................................................................ 140 Pareto Distribution.......................................................................... 140 Rayleigh Distribution....................................................................... 140 t Distribution..................................................................................... 141
Contents Triangular Distribution.....................................................................141 Uniform Distribution.........................................................................142 Weibull Distribution..........................................................................142 Distribution Parameters..........................................................................142 Average.............. ............................................................................... 142 Variance.............................................................................................142 Standard Deviation.......................................................................... 143 Standard Error..................................................................................143 Skewness.......................................................................................... 143 Standardized Skewness...................................................................143 Kurtosis................................................ ............................................143 Standardized Kurtosis.....................................................................143 Weighted Average............................................................................ 143 Estimation and Testing.........................................................................144 100(1 ֊ ct)% Confidence Interval for Mean....................................144 100(1 - ot)% Confidence Interval for Variance............................ 144 100(1 — a)% Confidence Interval for
Difference in Means.........144 Equal Variance........................................................................... 144 Unequal Variance.......................................................................144 100(1 - a)% Confidence Interval for Ratio of Variances............145 Normal Probability Plot................................................................. 145 Comparison of Poisson Rates.........................................................145 Distribution Functions and Parameter Estimation............................146 Bernoulli............................................................................................ 146 Binomial.......................................................................................... 146 Discrete Uniform............................................................................ 146 Geometric........................................................................................146 Negative Binomial.......................................................................... 146 Poisson............................................................................................. 146 Beta.................................................................................................. 146 Chi-Square.........................................................................................147 Erlang.................................................................................................147 Exponential........................................................................................147
F.......................................................................................................... 147 Gamma.............................................................................................. 147 Lognormal.........................................................................................148 System Displays................................................................................ 148 Normal............................................................................................... 148 Student’s t..........................................................................................148 Triangular..........................................................................................148 Uniform.............................................................................................149 Weibull..............................................................................................149 Chi-Square Test for Distribution Fitting........................................ 149 Kolmogorov-Smirnov Test............................................................. 149 ANOVA (Analysis of Variance)..................................................... 150 Notations...................................................................................... 150
Contents XV Standard Error (Internal)..........................................................151 Standard Error (Pooled)..............................................................151 Interval Estimates....................................................................... 151 Tukey Interval...................................................................................151 Scheffe Interval..............................................................................151 Cochran C-Test...............................................................................151 Bartlett Test......................................................................................152 Hartley’s Test....................................................................................152 Kruskal-Wallis Test........................................................................ 152 Freidman Test...................................................................................153 Regression....................................................................................... 154 Notations......................................................................................154 Regression Statistics...................................................................154 Predictions...................................................................................155 Nonlinear Regression.................................................................156 Ridge Regression........................................................................157 Quality
Control...........................................................................157 Subgroup Statistics.....................................................................157 X-Bar Charts............................................................................... 158 Capability Ratios........................................................................159 R Charts.......................................................................................159 S Charts........................................................................................160 C Charts.......................................................................................160 U Charts.......................................................................................160 P Charts.......................................................................................160 NP Charts.................................................................................... 161 CuSum Chart for the Mean....................................................... 161 Multivariate Control Charts....................................................... 162 Time Series Analysis.......................................................................162 Notations......................................................................................162 Autocorrelation at Lag к.............................................................162 Partial Autocorrelation at Lag к................................................163 Cross-Correlation at Lag к......................................................... 163 Box-
Cox.......................................................................................163 Periodogram (Computed Using Fast Fourier Transform)...... 164 Categorical Analysis........................................................................ 164 Notations......................................................................................164 Totals............................................................................................ 164 Chi-Square...................................................................................165 Fisher’s Exact Test...................................................................... 165 Lambda........................................................................................ 165 Uncertainty Coefficient...............................................................165 Somer’s D.....................................................................................166 Eta.................................................................................................167 Contingency Coefficient.............................................................167 Cramer’s V...................................................................................168
XVI Contents Conditional Gamma................................................................. 168 Pearson’s r............................................................................... 168 Kendall’s Таи Ъ....................................................................... 168 Tau C.........................................................................................168 Probability Terminology............................................................... 168 Basic Probability Principles......................................................... 169 Random Variable...........................................................................169 Mean Value x or Expected Value μ............................................. 169 Discrete Distribution Formulas......................................................... 170 Bernoulli Distribution.................................................................. 170 Beta Binomial Distribution.........................................................170 Beta Pascal Distribution..............................................................171 Binomial Distribution.................................................................. 171 Discrete Weibull Distribution......................................................171 Geometric Distribution................................................................171 Hypergeometric Distribution.......................................................171 Negative Binomial Distribution.................................................... 172 Poisson
Distribution....................................................................172 Rectangular (Discrete Uniform) Distribution............................ 173 Continuous Distribution Formulas..............................................173 Arcsin Distribution...................................................................... 173 Beta Distribution......................................................................... 173 Cauchy Distribution.....................................................................174 Chi Distribution...........................................................................174 Chi-Square Distribution..............................................................174 Erlang Distribution......................................................................174 Exponential Distribution.............................................................. 175 Extreme-Value Distribution.......................................................... 175 F Distribution................................................................................ 175 Gamma Distribution..................................................................... 176 Half-Normal Distribution............................................................. 176 Laplace (Double Exponential) Distribution.................................176 Logistic Distribution.....................................................................177 Lognormal Distribution................................................................177 Noncentral Chi-Square
Distribution............................................177 Noncentral F Distribution............................................................178 Noncentral t Distribution..............................................................178 Normal Distribution.....................................................................178 Pareto Distribution.......................................................................179 Rayleigh Distribution....................................................................179 t Distribution.................................................................................179 Triangular Distribution................................................................ 180 Uniform Distribution....................................................................180 Weibull Distribution.................................................................... 180 Variate Generation Techniques....................................................181 Reference...........................................................................................183
Contents Chapter 6 xvii Descriptive Statistics for Data Presentation......................................185 Introduction......................................................................................... 185 Sample Average............................................................................... 185 Sample Variance.............................................................................. 185 Sample Standard Deviation............................................................ 186 Sample Standard Errorof the Mean................................................187 Skewness.................................................................................... 187 Standardized Skewness............................................................188 Kurtasis...................................................................................... 188 Standardized Kurtasis.............................................................. 188 Weighted Average..................................................................... 188 Estimation and Testing......................................................................... 188 100(1 — a)% Confidence Intervalfor Mean....................................188 100(1 — a)% Confidence Intervalfor Variance.............................. 188 100(1 — a)% Confidence Interval forDifference in Means.......188 For Equal Variance.....................................................................188 For Unequal Variance.................................................................189 100(1 — a)% Confidence Interval forRatio of
Variances..........189 Normal Probability Plot..................................................................189 Comparison of Poisson Rates......................................................... 190 Distribution functions and Parameter Estimation..............................190 Bernoulli Distribution.....................................................................190 Binomial Distribution......................................................................190 Discrete Uniform Distribution........................................................ 190 Geometric Distribution....................................................................190 Negative Binomial Distribution...................................................... 191 Poisson Distribution........................................................................ 191 Beta Distribution............................................................................. 191 Chi-Square Distribution..................................................................191 Erlang Distribution.......................................................................... 191 Exponential Distribution.................................................................192 F Distribution................................................................................... 192 Gamma Distribution........................................................................192 Lognormal Distribution...................................................................192 Normal
Distribution........................................................................193 Student’s t.........................................................................................193 Triangular Distribution....................................................................193 Uniform Distribution....................................................................... 193 Weibull Distribution........................................................................ 193 Chi-Square Test for DistributionFitting........................................ 194 Kolmogorov-Smirnov Test............................................................ 194 ANOVA (Analysis of Variance)..................................................... 194 Notations......................................................................................194 Standard Error............................................................................ 195 Interval Estimates....................................................................... 195
xviii Contents Tukey Interval.............................................................................. 195 Scheffe Interval........................................................................... 196 Cochran C-test.............................................................................. 196 Bartlett Test.................................................................................. 196 Hartley’s Test................................................................................ 196 Kruskal-Wallis Test..................................................................... 197 Freidman Test............................................................................... 197 Regression..................................................................................... 198 Notations.................................................................................. 198 Statistical Quality Control..................................................... 199 Subgroup Statistics.................................................................199 X-Bar Charts.......................................................................... 199 Capability Ratios.................................................................... 200 R Charts...................................................................................201 S Charts...................................................................................201 C Charts...................................................................................201 U
Charts...................................................................................201 P Charts...................................................................................201 NP Charts.............................................................................. 202 CuSum Chart for the Mean...................................................202 Time Series Analysis..................................................................203 Notations................................................................................203 Autocorrelation at Lag к....................................................... 203 Partial Autocorrelation at Lag к........................................... 203 Cross-Correlation at Lag к.................................................... 203 Box-Cox Computation.......................................................... 204 Periodogram (Computed Using Fast Fourier Transform)......204 Categorical Analysis.................................................................. 205 Notations............................................................................... 205 Totals..................................................................................... 205 Chi-Square............................................................................205 Lambda................................................................................... 205 Uncertainty Coefficient...........................................................206 Somer’s D Measure................................................................. 206
Eta........................................................................................... 207 Contingency Coefficient.........................................................208 Cramer’s V Measure...............................................................208 Conditional Gamma................................................................ 208 Pearson’s r Measure................................................................ 208 Kendall’s Tau b Measure........................................................208 Tau C Measure........................................................................209 Overall Mean..........................................................................209 Cheby shev’s Theorem.............................................................209 Permutation.............................................................................209 Combination...........................................................................209 Failure.....................................................................................209
Contents Chapter 7 xix Data Analytics Tools for Understanding Random Field Regression Models............................................................................... 211 Introduction...........................................................................................211 RFR Models......................................................................................... 212 Two Examples...................................................................................... 214 Bayesian Regression Models and Random Fields..............................214 Data Analysis: Finding the Associated Regression Model...............215 Relating Eigenvectors to Regression Functions................................ 223 Some Special Random Field Models................................................. 225 Gaussian Covariance as Damped Polynomial Regression................225 Trigonometric Regression and Spline Covariance............................ 227 Discussion............................................................................................. 228 References............................................................................................ 229 Chapter 8 Application of DEJI Systems Model to Data Integration..................233 Introduction to Data Integration..........................................................233 Leveraging the Input-Control-Output-Mechanism Model................234 Data Types and Fidelity....................................................................... 235 Data Collection and
Sanitization.........................................................236 DEJI Systems Model for Data Quality............................................... 238 Data Value Model.................................................................................239 Data Quality Control........................................................................... 241 References............................................................................................ 242 Index 243
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Contents Preface. xxi Acknowledgments.xxiii Author.xxv Chapter 1 Essentials of Data Analytics. I Introduction to COVID-19 Data Analytics. 1 Systems View of Data Analytics.2 Global Growth of Data Analytics.2 Background in Predictive Analytics.3 Data Modeling Approaches. 5 Data Fanaticism. 6 Data and Measurements for Data Analytics.7 What Is Measurement?. 7 Data Measurement Systems. 8 Fundamental Scientific Equations.11 Einstein’s Equation. 11 Einstein’s Field Equation.11 Heisenberg’s Uncertainty
Principle. 12 Schrödinger Equation. 12 Dirac Equation. 12 Maxwell’s Equations. 13 Boltzmann’s Equation for Entropy. 13 Planck-Einstein Equation. 13 Planck’s Blackbody Radiation Formula. 14 Hawking Equation for Black Hole Temperature. 14 Navier-Stokes Equation for a Fluid.14 Lagrangian for Quantum Chromodynamics. 14 Bardeen-Cooper-Schrieffer Equation for Superconductivity. 15 Josephson Effect. 15 Fermat’s Last Theorem. 15 Methods for Data Measurement and Comparison. 16 Direct Comparison. 16 Indirect Comparison. 17 Data Measurement Scales. 17 Nominal Scale of Measurement.18 Ordinal Scale of Measurement. 18 Interval Scale of Measurement. 18
Ratio Scale Measurement. 18 Reference Units of Measurements. 19 Common Constants.20 Numeric Data Representation.20 vii
viii Contents The Language of Data Analytics. 21 Quick Reference for Mathematical Equations.21 Reference. 28 Chapter 2 Empirical Model Building.29 Introduction to the Model Environment. 29 State-Space Modeling.30 Calculus Reference for Data Analytics. 32 Integration Rules. 33 Solving Integrals with Variable Substitution.34 Riemann Integral. 34 Integration by Parts.34 Compound Functions Where the Inner Function Is ax. 34 Integration by Parts. 35 Systems Modeling for Data Analytics. 36 Triple C Questions. 39 Communication. 40
Cooperation.45 Coordination.47 Conflict Resolution in Data Analytics. 47 References.49 Chapter 3 Data Visualization Methods. 51 Introduction to Data Visualization.51 Case Example of “Covidvisualizer” Website.51 Dynamism and Volatility of Data.52 Data Determination and Collection. 53 Choosing the Data. 53 Collecting the Data. 53 Relevance Check. 54 Limit Check.54 Critical Value.54 Coding the Data. 54 Processing the Data.54 Control
Total. 54 Consistency Check. 55 Scales of Measurement. 55 Using the Information. 55 Data Exploitation.57 Raw Data. 57 Total Revenue.58 Average Revenue. 59 Median Revenue. 61 Quartiles and Percentiles. 62
Contents IX The Mode. 63 Range of Revenue. 63 Average Deviation. 63 Sample Variance. 64 Standard Deviation. 65 Chapter 4 Basic Mathematical Calculations for Data Analytics.69 Introduction to Calculation for Data Analytics.69 Quadratic Equation. 69 Overall Mean. 70 Chebyshev’s Theorem. 70 Permutations. 70 Combinations. 70 Failure. 71 Probability Distribution. 71 Probability. 71 Distribution Function. 71 Expected Value. 72
Variance. 72 Binomial Distribution. 73 Poisson Distribution. 73 Mean of a Binomial Distribution. 73 Variance. 73 Normal Distribution. 73 Cumulative Distribution Function.73 Population Mean. 73 Standard Error of the Mean.74 f֊Distribution. 74 Chi-Squared Distribution.74 Definition of Set and Notation.74 Set Terms and Symbols. 75 Venn Diagrams. 75 Operations on Sets. 76 De Morgan’s Laws. 76 Probability Terminology. 77 Basic Probability
Principles. 77 Random Variable. 77 Mean Value x or Expected Value μ.78 Series Expansions. 78 Mathematical Signs and Symbols.81 Greek Alphabet. 83 Algebra.83 Laws of Algebraic Operations.83 Special Products and Factors.83 Powers and Roots.85
x Contents Proportion. 85 Arithmetic Mean of n Quantities A. 86 Geometric Mean of n Quantities G.86 Harmonic Mean of n Quantities H. 86 Generalized Mean. 86 Solution of Quadratic Equations.87 Solution of Cubic Equations. 87 Trigonometric Solution of the Cubic Equation. 88 Solution of Quadratic Equations. 89 Partial Fractions.89 Non-repeated Linear Factors. 89 Repeated Linear Factors.90 General Terms. 90 Repeated Linear Factors. 91 Factors of Higher Degree. 91 Geometry.91
Triangles.91 Right Triangle. 92 Equilateral Triangle.92 General Triangle.92 Menelaus’s Theorem. 93 Ceva’s Theorem. 93 Quadrilaterals.93 Rectangle.93 Parallelogram. 94 Rhombus.94 Trapezoid.94 General Quadrilateral. 94 Regular Polygon of n Sides Each of Length b. 95 Regular Polygon of n Sides Inscribed in a Circle of Radius r. 95 Regular Polygon of n Sides Circumscribing a Circle of Radius r.,.,95 Cyclic Quadrilateral. 95 Prolemy’s
Theorem. 96 Cyclic-Inscriptable Quadrilateral. 96 Planar Areas by Approximation.97 Trapezoidal Rule. 97 Durand’s Rule. 97 Simpson’s Rule (n even). 97 Weddle’s Rule (n = 6).98 Solids Bounded by Planes.98 Cube. 98 Rectangular Parallelepiped (or Box). 98 Prism. 98 Pyramid. 98 Prismatoid. 99 Regular Polyhedra. 99
Contents xi Sphere of Radius r. 100 Right Circular Cylinder of Radius r andHeight h. 100 Circular Cylinder of Radius r and Slant Height í. 100 Cylinder of Cross-Sectional Area A andSlant Height і. 100 Right Circular Cone of Radius r and Height h. 101 Spherical Cap of Radius r and Height h. 101 Frustum of Right Circular Cone of Radii a, b and Height h. 101 Zone and Segment of Two Bases.101 Lune.101 Spherical Sector.101 Spherical Triangle and Polygon.101 Spheroids. 102 Ellipsoid. 102 Oblate Spheroid. 102 Prolate Spheroid. 102 Circular Torus. 102 Formulas from Plane Analytic Geometry.102 Distance d between Two Points. 102
Slope m of Line Joining Two Points.103 Equation of Line Joining Two Points.103 Equation of Line in Terms of x Intercept аФ 0 and у intercept Եփ 0.103 Normal Form for Equation of Line. 103 General Equation of Line.103 Distance from Point (x։, yt ) to Line Ax + By + C = 0. 103 Angle ψ between Two Lines Having Slopes mt and m2. 103 Area of Triangle with Verticles. 104 Transformation of Coordinates Involving Pure Translation. 104 Transformation of Coordinates Involving Pure Rotation.104 Transformation of Coordinates Involving Translation and Rotation. 104 Polar Coordinates (г, Θ).105 Plane Curves. 105 Catenary, Hyperbolic Cosine.105 Cardioid. 105 Circle.105 Cassinian
Curves.105 Cotangent Curve. 106 Cubical Parabola.106 Cosecant Curve.106 Cosine Curve. 106 Ellipse. 106 Gamma Function.106 Hyperbolic Functions. 106 Inverse Cosine Curve. 107 Inverse Sine Curve. 107
XII Contents Inverse Tangent Curve. 107 Logarithmic Curve.107 Parabola. 107 Cubical Parabola. 107 Tangent Curve. 107 Ellipsoid.107 Elliptic Cone. 107 Elliptic Cylinder.107 Hyperboloid of One Sheet.108 Elliptic Paraboloid.108 Hyperboloid of Two Sheets. 108 Hyperbolic Paraboloid.108 Sphere.108 Distance d between Two Points.108 Equations of Line Joining Ρ։(χ b y,, z։)and P2(x2, yշ, z2) in Standard Form. 108 Equations of Line Joining Vi, Z\ ) and
P2(x2, y2, z2) in Parametric Form.108 Angle j between Two Lines with Direction Cosines A, m,, щ and 1շ,1Ոշ,Ոշ.108 General Equation of a Plane. 109 Equation of Plane Passing through Points.109 Equation of Plane in Intercept Form. 109 Equations of Line through (x0 Vo · Zo) and Perpendicular to Plane.109 Distance from Point (x, y, z) to Plane Ax + By + D = 0.109 Normal form for Equation of Plane.109 Transformation of Coordinates Involving Pure Translation. 110 Transformation of Coordinates Involving Pure Rotation.110 Transformation of Coordinates Involving Translation and Rotation. 110 Cylindrical Coordinates (г, Θ, z). Ill Spherical Coordinates (г, Θ,. Ill Logarithmic Identities.112 Special Values.112 Logarithms to General
Base. 112 Series Expansions. 113 Limiting Values. 113 Inequalities.113 Continued Fractions. 114 Polynomial Approximations. 114 Fundamental Properties.115 Definition of General Powers. 116 Logarithmic and Exponential Functions. 116 Polynomial Approximations. 117 Slopes. 125
Contents xiii Trigonometric Ratios.125 Sine Law. 127 Cosine Law.127 Algebra. 127 Expanding.127 Factoring. 127 Roots of Quadratic.128 Law of Exponents. 128 Logarithms.128 Chapter 5 Statistical Methods for Data Analytics.129 Introduction.129 Discrete Distributions.129 Bernoulli Distribution.129 Beta Binomial Distribution. 129 Beta Pascal Distribution.132 Binomial
Distribution.132 Discrete Weibul! Distribution. 132 Geometric Distribution.132 Hypergeometric Distribution. 133 Negative Binomial Distribution. 133 Poisson Distribution.134 Rectangular (Discrete Uniform) Distribution. 134 Continuous Distributions.134 Arcsin Distribution. 134 Beta Distribution. 135 Cauchy Distribution. 135 Chi Distribution. 135 Chi-Square Distribution.135 Erlang Distribution. 136 Exponential Distribution.136 Extreme-Value Distribution.136 F Distribution.136 Gamma
Distribution. 137 Half-Normal Distribution.137 Laplace (Double Exponential) Distribution. 138 Logistic Distribution. 138 Lognormal Distribution.138 Noncentral Chi-Square Distribution.139 Noncentral F Distribution.139 Noncentral f Distribution.139 Normal Distribution. 140 Pareto Distribution. 140 Rayleigh Distribution. 140 t Distribution. 141
Contents Triangular Distribution.141 Uniform Distribution.142 Weibull Distribution.142 Distribution Parameters.142 Average. . 142 Variance.142 Standard Deviation. 143 Standard Error.143 Skewness. 143 Standardized Skewness.143 Kurtosis. .143 Standardized Kurtosis.143 Weighted Average. 143 Estimation and Testing.144 100(1 ֊ ct)% Confidence Interval for Mean.144 100(1 - ot)% Confidence Interval for Variance. 144 100(1 — a)% Confidence Interval for
Difference in Means.144 Equal Variance. 144 Unequal Variance.144 100(1 - a)% Confidence Interval for Ratio of Variances.145 Normal Probability Plot. 145 Comparison of Poisson Rates.145 Distribution Functions and Parameter Estimation.146 Bernoulli. 146 Binomial. 146 Discrete Uniform. 146 Geometric.146 Negative Binomial. 146 Poisson. 146 Beta. 146 Chi-Square.147 Erlang.147 Exponential.147
F. 147 Gamma. 147 Lognormal.148 System Displays. 148 Normal. 148 Student’s t.148 Triangular.148 Uniform.149 Weibull.149 Chi-Square Test for Distribution Fitting. 149 Kolmogorov-Smirnov Test. 149 ANOVA (Analysis of Variance). 150 Notations. 150
Contents XV Standard Error (Internal).151 Standard Error (Pooled).151 Interval Estimates. 151 Tukey Interval.151 Scheffe Interval.151 Cochran C-Test.151 Bartlett Test.152 Hartley’s Test.152 Kruskal-Wallis Test. 152 Freidman Test.153 Regression. 154 Notations.154 Regression Statistics.154 Predictions.155 Nonlinear Regression.156 Ridge Regression.157 Quality
Control.157 Subgroup Statistics.157 X-Bar Charts. 158 Capability Ratios.159 R Charts.159 S Charts.160 C Charts.160 U Charts.160 P Charts.160 NP Charts. 161 CuSum Chart for the Mean. 161 Multivariate Control Charts. 162 Time Series Analysis.162 Notations.162 Autocorrelation at Lag к.162 Partial Autocorrelation at Lag к.163 Cross-Correlation at Lag к. 163 Box-
Cox.163 Periodogram (Computed Using Fast Fourier Transform). 164 Categorical Analysis. 164 Notations.164 Totals. 164 Chi-Square.165 Fisher’s Exact Test. 165 Lambda. 165 Uncertainty Coefficient.165 Somer’s D.166 Eta.167 Contingency Coefficient.167 Cramer’s V.168
XVI Contents Conditional Gamma. 168 Pearson’s r. 168 Kendall’s Таи Ъ. 168 Tau C.168 Probability Terminology. 168 Basic Probability Principles. 169 Random Variable.169 Mean Value x or Expected Value μ. 169 Discrete Distribution Formulas. 170 Bernoulli Distribution. 170 Beta Binomial Distribution.170 Beta Pascal Distribution.171 Binomial Distribution. 171 Discrete Weibull Distribution.171 Geometric Distribution.171 Hypergeometric Distribution.171 Negative Binomial Distribution. 172 Poisson
Distribution.172 Rectangular (Discrete Uniform) Distribution. 173 Continuous Distribution Formulas.173 Arcsin Distribution. 173 Beta Distribution. 173 Cauchy Distribution.174 Chi Distribution.174 Chi-Square Distribution.174 Erlang Distribution.174 Exponential Distribution. 175 Extreme-Value Distribution. 175 F Distribution. 175 Gamma Distribution. 176 Half-Normal Distribution. 176 Laplace (Double Exponential) Distribution.176 Logistic Distribution.177 Lognormal Distribution.177 Noncentral Chi-Square
Distribution.177 Noncentral F Distribution.178 Noncentral t Distribution.178 Normal Distribution.178 Pareto Distribution.179 Rayleigh Distribution.179 t Distribution.179 Triangular Distribution. 180 Uniform Distribution.180 Weibull Distribution. 180 Variate Generation Techniques.181 Reference.183
Contents Chapter 6 xvii Descriptive Statistics for Data Presentation.185 Introduction. 185 Sample Average. 185 Sample Variance. 185 Sample Standard Deviation. 186 Sample Standard Errorof the Mean.187 Skewness. 187 Standardized Skewness.188 Kurtasis. 188 Standardized Kurtasis. 188 Weighted Average. 188 Estimation and Testing. 188 100(1 — a)% Confidence Intervalfor Mean.188 100(1 — a)% Confidence Intervalfor Variance. 188 100(1 — a)% Confidence Interval forDifference in Means.188 For Equal Variance.188 For Unequal Variance.189 100(1 — a)% Confidence Interval forRatio of
Variances.189 Normal Probability Plot.189 Comparison of Poisson Rates. 190 Distribution functions and Parameter Estimation.190 Bernoulli Distribution.190 Binomial Distribution.190 Discrete Uniform Distribution. 190 Geometric Distribution.190 Negative Binomial Distribution. 191 Poisson Distribution. 191 Beta Distribution. 191 Chi-Square Distribution.191 Erlang Distribution. 191 Exponential Distribution.192 F Distribution. 192 Gamma Distribution.192 Lognormal Distribution.192 Normal
Distribution.193 Student’s t.193 Triangular Distribution.193 Uniform Distribution. 193 Weibull Distribution. 193 Chi-Square Test for DistributionFitting. 194 Kolmogorov-Smirnov Test. 194 ANOVA (Analysis of Variance). 194 Notations.194 Standard Error. 195 Interval Estimates. 195
xviii Contents Tukey Interval. 195 Scheffe Interval. 196 Cochran C-test. 196 Bartlett Test. 196 Hartley’s Test. 196 Kruskal-Wallis Test. 197 Freidman Test. 197 Regression. 198 Notations. 198 Statistical Quality Control. 199 Subgroup Statistics.199 X-Bar Charts. 199 Capability Ratios. 200 R Charts.201 S Charts.201 C Charts.201 U
Charts.201 P Charts.201 NP Charts. 202 CuSum Chart for the Mean.202 Time Series Analysis.203 Notations.203 Autocorrelation at Lag к. 203 Partial Autocorrelation at Lag к. 203 Cross-Correlation at Lag к. 203 Box-Cox Computation. 204 Periodogram (Computed Using Fast Fourier Transform).204 Categorical Analysis. 205 Notations. 205 Totals. 205 Chi-Square.205 Lambda. 205 Uncertainty Coefficient.206 Somer’s D Measure. 206
Eta. 207 Contingency Coefficient.208 Cramer’s V Measure.208 Conditional Gamma. 208 Pearson’s r Measure. 208 Kendall’s Tau b Measure.208 Tau C Measure.209 Overall Mean.209 Cheby shev’s Theorem.209 Permutation.209 Combination.209 Failure.209
Contents Chapter 7 xix Data Analytics Tools for Understanding Random Field Regression Models. 211 Introduction.211 RFR Models. 212 Two Examples. 214 Bayesian Regression Models and Random Fields.214 Data Analysis: Finding the Associated Regression Model.215 Relating Eigenvectors to Regression Functions. 223 Some Special Random Field Models. 225 Gaussian Covariance as Damped Polynomial Regression.225 Trigonometric Regression and Spline Covariance. 227 Discussion. 228 References. 229 Chapter 8 Application of DEJI Systems Model to Data Integration.233 Introduction to Data Integration.233 Leveraging the Input-Control-Output-Mechanism Model.234 Data Types and Fidelity. 235 Data Collection and
Sanitization.236 DEJI Systems Model for Data Quality. 238 Data Value Model.239 Data Quality Control. 241 References. 242 Index 243 |
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| index_date | 2024-07-03T16:13:41Z |
| indexdate | 2024-07-10T09:01:46Z |
| institution | BVB |
| isbn | 9780367537418 |
| language | English |
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| physical | xxv,246 Seiten Diagramme |
| publishDate | 2020 |
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| publisher | CRC Press |
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| spelling | Badiru, Adedeji Bodunde 1952- Verfasser (DE-588)124156665 aut Data analytics handbook of formulas and techniques Adedeji B. Badiru London CRC Press 2020 xxv,246 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Systems innovation book series Datenanalyse (DE-588)4123037-1 gnd rswk-swf Datenmodell (DE-588)4192516-6 gnd rswk-swf Datenanalyse (DE-588)4123037-1 s Datenmodell (DE-588)4192516-6 s b DE-604 Erscheint auch als Online-Ausgabe 978-1-003-08314-6 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032477993&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Badiru, Adedeji Bodunde 1952- Data analytics handbook of formulas and techniques Datenanalyse (DE-588)4123037-1 gnd Datenmodell (DE-588)4192516-6 gnd |
| subject_GND | (DE-588)4123037-1 (DE-588)4192516-6 |
| title | Data analytics handbook of formulas and techniques |
| title_auth | Data analytics handbook of formulas and techniques |
| title_exact_search | Data analytics handbook of formulas and techniques |
| title_exact_search_txtP | Data analytics handbook of formulas and techniques |
| title_full | Data analytics handbook of formulas and techniques Adedeji B. Badiru |
| title_fullStr | Data analytics handbook of formulas and techniques Adedeji B. Badiru |
| title_full_unstemmed | Data analytics handbook of formulas and techniques Adedeji B. Badiru |
| title_short | Data analytics |
| title_sort | data analytics handbook of formulas and techniques |
| title_sub | handbook of formulas and techniques |
| topic | Datenanalyse (DE-588)4123037-1 gnd Datenmodell (DE-588)4192516-6 gnd |
| topic_facet | Datenanalyse Datenmodell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032477993&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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