Understanding Statistics and Probability: An Introduction to Methods, Techniques and Computer Applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
North Charleston
CreateSpace
2017
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| Ausgabe: | 1st edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 659 Seiten Illustrationen, Diagramme |
| ISBN: | 9781540622594 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | Contents I Exploratory and Descriptive Data Analysis 1 Introduction 21 23 1.1 Goals of Exploratory Data Analysis...................................................... 23 1.2 Fundamental Concepts: Variables, Observations, and Scaling..............24 2 One-Dimensional Data Analysis 2.1 2.2 2.3 2.4 2.5 2.6 33 Observed Frequencies and Empirical Distributions.............................. 33 Location Measures.................................................................................... 40 Dispersion Measures ...............................................................................51 Skewness and Kurtasis Measures............................................................ 59 Boxplots.................................................................................................... 63 Exercises................................................... 69 3 Two-Dimensional Data Analysis 71 3.1 Joint Empirical Distributions................................................................. 71 3.2 Association, Correlation and Dependence Measures.............................. 76 3.3 Exercises.................................................................................................... 92 4 Inequality and Concentration Measurement 4.1 4.2 4.3 4.4 95 Introduction...............................................................................................95 The Lorenz Curve..................................................................................98 The Gini Coefficient................................................................................ 103
Exercises................................................................................................... 109 5 Indices 111 5.1 Introduction..............................................................................................Ill 5.2 Price Indices . ........................................................................................... 112 5.2.1 Price Index due to Laspeyres ..................................................... 112 5.2.2 Price Index due to Paasche...........................................................113 5.2.3 Discussion......................................................................................115 5.3 Quantitative and Sales Indices ............................................................. 116 5.4 Exercises................................................................................................... 117 15
Contents II Stochastics and Probability 119 6 Basics of Probability Theory 121 6.1 Sets................................................................................. 122 6.2 Random Experiments, Events, and Probabilities.................................. 127 6.3 Probability Concepts................................................................................ 131 6.3.1 Objective or Frequentistic Probabilities..................................... 131 6.3.2 Subjective Probabilities................................................................ 135 6.3.3 Some Computational Rules ........................................................ 135 6.4 Conditional Probabilities........................................................................ 137 6.5 Dependence and Independence ............................................................. 138 6.6 The Total Probability Rule................ 139 6.7 Bayes’ Rule.............................................................................................. 141 6.8 Sampling................................................................. 147 6.9 Exercises................................................................................................... 159 7 Random Variables 163 7.1 One-Dimensional Random Variables..................................................... 163 7.1.1 Definition of Random Variables...................................................163 7.1.2 Characterization of Random Variables........................................166 7.1.3 Expectation, Variance and Standard Deviation ....................... 175 7.1.4
Covariance, Correlation, and Linear Combinations..................178 7.1.5 Some Important Discrete Distributions..................................... 179 7.1.6 Some Important Continuous Distributions................................192 7.1.7 Moments ......................................................................................231 7.1.8 Moment Generating Function..................................................... 239 7.1.9 Transformations and Functions of Random Variables............... 240 7.1.10 Central Limit Theorem................................................................ 251 7.2 Multi-Dimensional Random Variables.................................................. 257 7.2.1 Definition and Characterization of Multi-Dimensional Ran dom Variables ........................ 257 7.2.2 Dependence, Conditional Distributions, and Correlation .... 261 7.2.3 Multivariate Expectations, Variances and Covariances...........269 7.2.4 Special Case: Bivariate Normal Distribution.............................270 7.3 Exercises................................................................................................... 278 III Inferential Statistics 8 Basics of Statistical Estimation 283 287 8.1 Random Sampling and Estimation........................................................287 8.2 Properties of Estimators .............................................. 290 16
Contents 8.3 Methods for Point Estimation................................................................301 8.3.1 Method of Moments..................................................................... 301 8.3.2 Least Squares Method................................................................302 8.3.3 Maximum Likelihood Method.....................................................305 8.4 Interval Estimation................................................................................317 8.4.1 Markov’s and Chebychev’s Inequalities.....................................318 8.4.2 Confidence Intervals for the Population Mean..........................319 8.4.3 Confidence Intervals for Proportions.......................................... 333 8.4.4 Confidence Intervals for Variances and Standard Deviations . 336 8.5 Exercises........................................................................................... 340 9 Hypothesis Testing 343 9.1 Basics of Statistical Hypothesis Testing................................................343 9.2 Statistical Decision Theory.............................................................. .. . 350 9.3 Some Frequently Encountered Testing Situations............................... 366 9.3.1 Tests for the Population Mean.....................................................366 9.3.2 Tests for the Population Proportion.............................................369 9.3.3 Comparisons of Means in Different Populations....................... 373 9.3.4 χ2 Goodness of Fit Test for One-Way Tables............................... 384 9.3.5 χ2
Independence Test for Two-Way Tables ................................390 9.3.6 Extensions ...................................................................................395 9.4 Exercises...................................................................................................396 IV Regression and Applied Data Analysis 401 10 Linear Regression 403 10.1 Basics of Regression and Statistical Model Building . .......................... 403 10.2 Model and Assumptions.......................................................................... 405 10.3 Model Estimation ...................................................................................409 10.4 Confidence Intervals, Testsand Predictions......................................... 417 10.4.1 Confidence Intervals .................................................................. 417 10.4.2 Tests............................................................................................. 418 10.4.3 Predictions...................................................................................418 10.5 Exercises...................................................................................................421 11 Multiple Regression 423 11.1 Model and Estimation............................................................................. 423 11.1.1 Model and Assumptions ............................................................. 423 11.1.2 Parameter Estimation ................................................................424 11.2 Testing and
Predicting...........................................................................428 11.2.1 Testing...........................................................................................428 17
Contents 11.2.2 Predictions................................................... 431 11.3 Regression Diagnostics...........................................................................434 11.3.1 Influential Points and Outliers.................................................. 434 11.3.2 Non-Linearity ............................................................................. 442 11.3.3 Heteroscedasticity........................................................................447 11.3.4 Autocorrelations and Clusters..................................................... 451 11.3.5 Non-Normality..............................................................................459 11.4 Regression with Quantitative and Qualitative Data............................ 464 11.5 Regression for Difference-in-Differences Analysis............................... 470 11.6 Model Estimation Using Maximum Likelihood.....................................475 11.7 Exercises............................................. 479 12 Analysis of Variance 483 12.1 One-way ANOVA................................................ 483 12.1.1 Basic Model...................................................................................484 12.1.2 Hypotheses and Tests...................................................................485 12.2 Two-way ANOVA......................................................................................491 12.2.1 Basic Model................................... 491 12.2.2 Hypotheses and Tests...................................................................493 12.3
Exercises................................................................................................... 501 13 Generalized Linear Models 503 13.1 Model and Link Functions.................................................................... 503 13.2 Some Specific Models..............................................................................507 13.2.1 Normal Distribution..................................................................... 507 13.2.2 Bernoulli and Binomial Distribution.......................................... 512 13.2.3 Poisson Distribution..................................................................... 517 13.2.4 Beta Distribution ........................................................................ 519 13.3 Exercises................................................................................................... 525 V Special Topics 14 Copulas 527 529 14.1 Definition of a Copula and Sklar’s Theorem.......................................... 529 14.2 Some Special Copulas..............................................................................531 14.3 Copula Densities......................................................................................539 14.4 Monte-Carlo Simulation of Copulas........................................................542 14.5 Advanced Dependence Measures...........................................................563 14.6 Copula Estimation Using the Maximum Likelihood Method............... 570 14.7 Exercises...................................................................... 580 18
Contents 15 Basics of Bayesian Statistics 581 15.1 Introduction............................................................................................. 581 15.2 The Bayesian Approach to Statistics.....................................................583 15.2.1 Bayes’ Theorem.......................................................................... 583 15.2.2 Point and Interval Estimation.....................................................588 15.2.3 Forecasting...................................................................................590 15.2.4 Model Comparison........................................................................591 15.2.5 Bayesian Model Averaging.......................................................... 592 15.2.6 Prior Distributions ........................................... 593 15.2.7 Likelihood.............................................................................. 594 15.2.8 Hierarchical Models..................................................................... 594 15.3 Applications............................................................................................. 595 15.3.1 Application 1: Linear Regression................................................595 15.3.2 Application 2: Risk Management........................................... . 604 15.4 Exercises...................................................................................................610 16 Epilogue: Statistical Fallacies 613 16.1 Computational and Psychological Fallacies.......................................... 613 16.2 Empirical
Fallacies...................................................................................614 16.2.1 False Causality............................................................................. 614 16.2.2 Regression to the Mean................................................................615 16.2.3 Data Mining........................... 619 16.2.4 Hindsight Bias............................................................................. 624 16.2.5 Pseudoreplication........................................................................624 Appendices 625 A Introduction to SAS Software A.1 A.2 A.3 A.4 627 Basics ..................................................................................................... 627 Starting SAS...........................................................................................628 Basic Language Conventions.............................................................. . 629 Working with SAS...................................................................................632 В Statistical Tables 635 B.l Table for the cumulative distribution function Ф of the standard nor mal distribution ..................................................................................... 636 B.2 Table for the 1 - a-quantiles of theT distribution.................................637 B.3 Table for the 1 - a-quantiles of theχ2 distribution................................ 638 Bibliography 639 List of Figures 643 19
Contents List of Key Words 20 654
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| spelling | Rösch, Daniel 1968- Verfasser (DE-588)171503228 aut Understanding Statistics and Probability An Introduction to Methods, Techniques and Computer Applications Daniel Rösch 1st edition North Charleston CreateSpace 2017 659 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Statistik (DE-588)4056995-0 s Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s b DE-604 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=029939158&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Understanding Statistics and Probability An Introduction to Methods, Techniques and Computer Applications |
| title_auth | Understanding Statistics and Probability An Introduction to Methods, Techniques and Computer Applications |
| title_exact_search | Understanding Statistics and Probability An Introduction to Methods, Techniques and Computer Applications |
| title_full | Understanding Statistics and Probability An Introduction to Methods, Techniques and Computer Applications Daniel Rösch |
| title_fullStr | Understanding Statistics and Probability An Introduction to Methods, Techniques and Computer Applications Daniel Rösch |
| title_full_unstemmed | Understanding Statistics and Probability An Introduction to Methods, Techniques and Computer Applications Daniel Rösch |
| title_short | Understanding Statistics and Probability |
| title_sort | understanding statistics and probability an introduction to methods techniques and computer applications |
| title_sub | An Introduction to Methods, Techniques and Computer Applications |
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| topic_facet | Wahrscheinlichkeitsrechnung Statistik Lehrbuch |
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