Probability, statistics and other frightening stuff: Alan R. Jones
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Routledge
2019
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| Schriftenreihe: | Working guides to estimating & forecasting series
Volume 2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xxvii, 471 Seiten Illustrationen |
| ISBN: | 9781138065031 |
Internformat
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| 245 | 1 | 0 | |a Probability, statistics and other frightening stuff |b Alan R. Jones |
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| 300 | |a xxvii, 471 Seiten |b Illustrationen | ||
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Datensatz im Suchindex
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| adam_text | Contents
List of Figures xvii
List of Tables xxii
Foreword xxvi
1 Introduction and objectives 1
1.1 Why write this book? Who might find it useful? Why five volumes? 2
1.1.1 Why write this series? Who might find it useful? 2
1.1.2 Why five volumes? 2
1.2 Features you’ll find in this book and others in this series 3
1.2.1 Chapter context 3
1.2.2 The lighter side (humour) 3
1.2.3 Quotations 3
1.2.4 Definitions 4
1.2.5 Discussions and explanations with a mathematical
slant for Formula-philes 5
1.2.6 Discussions and explanations without a mathematical
slant for Formula-phobes 5
1.2.7 Caveat augur 6
1.2.8 Worked examples 6
1.2.9 Useful Microsoft Excel functions and facilities 6
1.2.10 References to authoritative sources 7
1.2.11 Chapter reviews 7
1.3 Overview of chapters in this volume 7
1A Elsewhere in the ‘Working Guide to Estimating Forecasting’ series 8
1.4.1 Volume I: Principles, Process and Practice of Professional
Number Juggling 9
1.4.2 Volume II: Probability, Statistics and Other Frightening Stuff 10
1.4.3 Volume III: Best Fit Lines and Curves, and
Some Mathe-Magical Transformations 10
X
Contents
1.4.4 Volume IV: Learning, Unlearning and Re-Learning Curves 11
1.4.5 Volume V: Risk, Opportunity, Uncertainty and Other
Random Models 12
1.5 Final thoughts and musings on this volume and series 13
References 14
2 Measures of Central Tendency: Means, Modes, Medians 15
2.1 ‘S’ is for shivers, statistics and spin 15
2.1.1 Cutting through the mumbo-jumbo:What is or are statistics? 16
2.1.2 Are there any types of statistics that are not ‘Descriptive? 17
2.1.3 Samples, populations and the dreaded statistical bias 17
2.2 Measures of Central Tendency 17
2.2.1 What do we mean by ‘Mean? 18
2.2.2 Can we take the average of an average? 19
2.3 Arithmetic Mean — the Simple Average 19
2.3.1 Properties of Arithmetic Means: A potentially
unachievable value! 21
2.3.2 Properties of Arithmetic Means: An unbiased representative
value of the whole 23
2.3.3 Why would we not want to use the Arithmetic Mean? 25
2.3.4 Is an Arithmetic Mean useful where there is an upward or
downward trend? 26
2.3.5 Average of averages: Can we take the Arithmetic Mean
of an Arithmetic Mean? 27
2.4 Geometric Mean 30
2.4.1 Basic rules and properties of a Geometric Mean 30
2.4.2 When might we want to use a Geometric Mean? 31
2.4.3 Finding a steady state rate of growth or decay with a
Geometric Mean 33
2.4.4 Using a Geometric Mean as a Cross-Driver Comparator 39
2.4.5 Using a Geometric Mean with certain Non-Linear
Regressions 39
2.4.6 Average of averages: Can we take the Geometric Mean of
a Geometric Mean? 40
2.5 Harmonic Mean 41
2.5.1 Surely estimators would never use the Harmonic Mean? 42
2.5.2 Cases where the Harmonic Mean and the Arithmetic Mean
are both inappropriate 45
2.5.3 Average of averages: Can we take the Harmonic Mean of
a Harmonic Mean? 45
2.6 Quadratic Mean: Root Mean Square 48
2.6.1 When would we ever use a Quadratic Mean? 48
2.7 Comparison of Arithmetic, Geometric, Harmonic
and Quadratic Means 51
Contents xi
2.8 Mode 52
2.8.1 When would we use the Mode instead of the
Arithmetic Mean? 54
2.8.2 What does it mean if we observe more than one Mode? 54
2.8.3 What if we have two modes that occur at adjacent values? 55
2.8.4 Approximating the theoretical Mode when there is no real
observable Mode! 56
2.9 Median 60
2.9.1 Primary use of the Median 61
2.9.2 Finding the Median 61
2.10 Choosing a representative value:The 5-Ms 62
2.10.1 Some properties of the 5-Ms 63
2.11 Chapter review 65
References 66
3 Measures of Dispersion and Shape 67
3.1 Measures of Dispersion or scatter around a central value 67
3.2 Minimum, Maximum and Range 68
3.3 Absolute Deviations 70
3.3.1 Mean or Average Absolute Deviation (AAD) 71
3.3.2 Median Absolute Deviation (MAD) 73
3.3.3 Is there a Mode Absolute Deviation? 77
3.3.4 When would we use an Absolute Deviation? 77
3.4 Variance and Standard Deviation 79
3.4.1 Variance and Standard Deviation — compensating for
small samples 84
3.4.2 Coefficient of Variation 91
3.4.3 The Range Rule — is it myth or magic? 93
3.5 Comparison of deviation-based Measures of Dispersion 99
3.6 Confidence Levels, Limits and Intervals 101
3.6.1 Open and Closed Confidence Level Ranges 104
3.7 Quantiles: Quartiles, Quintiles, Deciles and Percentiles 106
3.7.1 A few more words about Quartiles 109
3.7.2 A few thoughts about Quintiles 112
3.7.3 And a few words about Deciles 113
3.7.4 Finally, a few words about Percentiles 114
3.8 Other Measures of Shape: Skewness and Peakedness 115
3.8.1 Measures of Skewness 116
3.8.2 Measures of Peakedness or Flatness — Kurtosis 120
3.9 Chapter review 123
References 124
4 Probability Distributions 125
4.1 Probability 126
4.1.1 Discrete Distributions 127
Contents
4.1.2 Continuous Distributions 131
4.1.3 Bounding Distributions 137
4.2 Normal Distributions 138
4.2.1 What is a Normal Distribution? 138
4.2.2 Key properties of a Normal Distribution 139
4.2.3 Where is the Normal Distribution observed? When can,
or should, it be used? 143
4.2.4 Probability Density Function and Cumulative
Distribution Function 145
4.2.5 Key stats and facts about the Normal Distribution 146
4.3 Uniform Distributions 147
4.3.1 Discrete Uniform Distributions 147
4.3.2 Continuous Uniform Distributions 149
4.3.3 Key properties of a Uniform Distribution 150
4.3.4 Where is the Uniform Distribution observed? When can,
or should, it be used? 153
4.3.5 Key stats and facts about the Uniform Distribution 154
4.4 Binomial and Bernoulli Distributions 155
4.4.1 What is a Binomial Distribution? 155
4.4.2 What is a Bernoulli Distribution? 156
4.4.3 Probability Mass Function and Cumulative
Distribution Function 157
4.4.4 Key properties of a Binomial Distribution 159
4.4.5 Where is the Binomial Distribution observed? When can,
or should, it be used? 161
4.4.6 Key stats and facts about the Binomial Distribution 161
4.5 Beta Distributions 162
4.5.1 What is a Beta Distribution? 162
4.5.2 Probability Density Function and Cumulative
Distribution Function 164
4.5.3 Key properties of a Beta Distribution 167
4.5.4 PERT-Beta or Project Beta Distributions 169
4.5.5 Where is the Beta Distribution observed? When can,
or should, it be used? 174
4.5.6 Key stats and facts about the Beta Distribution 175
4.6 Triangular Distributions 176
4.6.1 What is a Triangular Distribution? 176
4.6.2 Probability Density Function and Cumulative
Distribution Function 176
4.6.3 Key properties of a Triangular Distribution 178
Contents j xiii
4.6.4 Where is the Triangular Distribution observed? When can,
or should, it be used? 185
4.6.5 Key stats and facts about the Triangular Distribution 185
4.7 Lognormal Distributions 186
4.7.1 What is a Lognormal Distribution? 186
4.7.2 Probability Density Function and Cumulative
Distribution Function 189
4.7.3 Key properties of a Lognormal Distribution 190
4.7.4 Where is the Lognormal Distribution observed? When can,
or should, it be used? 193
4.7.5 Key stats and facts about the Lognormal Distribution 194
4.8 Weibull Distributions 195
4.8.1 What is a Weibull Distribution? 195
4.8.2 Probability Density Function and Cumulative
Distribution Function 196
4.8.3 Key properties of a Weibull Distribu tion 198
4.8.4 Where is the Weibull Distribution observed? When can,
or should, it be used? 202
4.8.5 Key stats and facts about the Weibull Distribution 205
4.9 Poisson Distributions 207
4.9.1 What is a Poisson Distribution? 207
4.9.2 Probability Mass Function and Cumulative
Distribution Function 210
4.9.3 Key properties of a Poisson Distribution 210
4.9.4 Where is the Poisson Distribution observed? When can, or
should, it be used? 214
4.9.5 Key stats and facts about the Poisson Distribution 216
4.10 Gamma and Chi-Squared Distributions 217
4.10.1 What is a Gamma Distribution? 217
4.10.2 What is a Chi-Squared Distribution? 220
4.10.3 Probability Density Function and Cumulative
Distribution Function 220
4.10.4 Key properties of Gamma and Chi-Squared Distributions 223
4.10.5 Where are the Gamma and Chi-Squared Distributions used? 226
4.10.6 Key stats and facts about the Gamma and
Chi-Squared Distributions 228
4.11 Exponential Distributions 229
4.11.1 What is an Exponential Distribution? 229
4.11.2 Probability Density Function and Cumulative
Distribution Function 229
Contents
xiv
4.11.3 Key properties of an Exponential Distribution 230
4.11A Where is the Exponential Distribution observed? When
can, or should, it be used? 233
4.11.5 Key stats and facts about the Exponential Distribution 234
4.12 Pareto Distributions 235
4.12.1 What is a Pareto Distribution? 235
4.12.2 Probability Density Function and Cumulative
Distribution Function 235
4.12.3 The Pareto Principle: How does it fit in with the
Pareto Distribution? 237
4.12.4 Key properties of a Pareto Distribution 241
4.12.5 Where is the Pareto Distribution observed? When can,
or should, it be used? 246
4.12.6 Key stats and facts about the Pareto Distribution 249
4.13 Choosing an appropriate distribution 250
4.14 Chapter review 253
References 253
5 Measures of Linearity, Dependence and Correlation 255
5.1 Covariance 257
5.2 Linear Correlation or Measures of Linear Dependence 264
5.2.1 Pearson s Correlation Coefficient 264
5.2.2 Pearson s Correlation Coefficient — key properties
and limitations 270
5.2.3 Correlation is not causation 279
5.2.4 Partial Correlation:Time for some Correlation Chicken 281
5.2.5 Coefficient of Determination 282
5.3 Rank Correlation 284
5.3.1 Spearmans Rank Correlation Coefficient 286
5.3.2 If Spearman’s Rank Correlation is so much trouble,
why bother? 295
5.3.3 Interpreting Spearmans Rank Correlation Coefficient 297
5.3.4 Kendall s Tau Rank Correlation Coefficient 301
5.3.5 If Kendall s Tau Rank Correlation is so much trouble,
why bother? 307
5.4 Correlation: What if you want to ‘Push it not ‘Puli’ it? 311
5.4.1 The Pushy Pythagorean Technique or restricting the scatter
around a straight line 312
5.4.2 4 Controlling Partner’Technique 317
5.4.3 Equivalence of the Pushy Pythagorean and Controlling
Partner Techniques 322
5.4.4 ‘Equal Partners Technique 323
5.4.5 Copulas 328
Contents
xv
5.5 Chapter review 336
References 339
6 Tails of the unexpected (1): Hypothesis Testing 340
6.1 Hypothesis Testing 341
6.1.1 Tails of the unexpected 342
6.2 Z-Scores and Z-Tests 344
6.2.1 Standard Error 345
6.2.2 Example: Z-Testing the Mean value of a Normal
Distribution 350
6.2.3 Example: Z-Testing the Median value of a
Beta Distribution 352
6.3 Student’s t-Distribudon and t-Tests 356
6.3.1 Students t-Distribution 356
6.3.2 t-Tests 359
6.3.3 Performing a t-Test in Microsoft Excel on a single sample 361
6.3.4 Performing a t-Test in Microsoft Excel to compare
two samples 364
6.4 Mann-Whitney U-Tests 367
6.5 Chi-Squared Tests or ^2-Tests 371
6.5.1 Chi-Squared Distribution revisited 371
6.5.2 Chi-Squared Test 371
6.6 F-Distribution and F-Tests 375
6.6.1 F-Distribution 375
6.6.2 F-Test 377
6.6.3 Primary use of the F-Distribution 377
6.7 Checking for Normality 380
6.7.1 Q-Q Plots 380
6.7.2 Using a Chi-Squared Test for Normality 386
6.7.3 Using the Jarque-Bera Test for Normality 389
6.8 Chapter review 390
References 391
7 Tails of the unexpected (2): Outing the outliers 392
7.1 Outing the outliers: Detecting and dealing with outliers 392
7.1.1 Mitigation of Type I and Type II outlier errors 396
7.2 Tukey Fences 399
7.2.1 Tukey Slimline Fences — for larger samples and less
tolerance of outliers? 407
7.3 Chauvenet’s Criterion 408
7.3.1 Variation on Chauvenet’s Criterion for small sample
sizes (SSS) 413
7.3.2 Taking a Q-Q perspective on Chauvenet s Criterion for
small sample sizes (SSS)
414
xvi Contents
7.4 Peirces Criterion 416
7.5 Iglewicz and Hoaglin’s MAD Technique 419
7.6 Grubbs’Test 425
7.7 Generalised Extreme Studentised Deviate (GESD) 429
7.8 Dixon’s Q-Test 430
7.9 Doing the JB Swing — using Skewness and Excess Kurtosis to
identify outliers 432
7.10 Outlier tests — a comparison 437
7.11 Chapter review 440
References 440
Glossary of estimating and forecasting terms 443
Legend for Microsoft Excel Worked Example Tables in Greyscale 462
Index 463
|
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| spelling | Jones, Alan R. 1953- Verfasser (DE-588)1161098445 aut Probability, statistics and other frightening stuff Alan R. Jones London Routledge 2019 xxvii, 471 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Working guides to estimating & forecasting series Volume 2 Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s Statistik (DE-588)4056995-0 s DE-604 Erscheint auch als Onlineausgabe 978-1-315-16006-1 Working guides to estimating & forecasting series Volume 2 (DE-604)BV045215706 2 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030399013&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jones, Alan R. 1953- Probability, statistics and other frightening stuff Alan R. Jones Working guides to estimating & forecasting series Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
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| title | Probability, statistics and other frightening stuff Alan R. Jones |
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| title_full | Probability, statistics and other frightening stuff Alan R. Jones |
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| title_full_unstemmed | Probability, statistics and other frightening stuff Alan R. Jones |
| title_short | Probability, statistics and other frightening stuff |
| title_sort | probability statistics and other frightening stuff alan r jones |
| title_sub | Alan R. Jones |
| topic | Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Wahrscheinlichkeitsrechnung Statistik |
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