Statistical Distributions / Edition 4

Statistical Distributions / Edition 4

by Catherine Forbes
     
 

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ISBN-10: 0470390638

ISBN-13: 9780470390634

Pub. Date: 12/21/2010

Publisher: Wiley

A new edition of the trusted guide on commonly used statistical distributions

Fully updated to reflect the latest developments on the topic, Statistical Distributions, Fourth Edition continues to serve as an authoritative guide on the application of statistical methods to research across various disciplines. The book provides a concise presentation of popular

Overview

A new edition of the trusted guide on commonly used statistical distributions

Fully updated to reflect the latest developments on the topic, Statistical Distributions, Fourth Edition continues to serve as an authoritative guide on the application of statistical methods to research across various disciplines. The book provides a concise presentation of popular statistical distributions along with the necessary knowledge for their successful use in data modeling and analysis.

Following a basic introduction, forty popular distributions are outlined in individual chapters that are complete with related facts and formulas. Reflecting the latest changes and trends in statistical distribution theory, the Fourth Edition features:

  • A new chapter on queuing formulas that discusses standard formulas that often arise from simple queuing systems
  • Methods for extending independent modeling schemes to the dependent case, covering techniques for generating complex distributions from simple distributions
  • New coverage of conditional probability, including conditional expectations and joint and marginal distributions
  • Commonly used tables associated with the normal (Gaussian), student-t, F and chi-square distributions
  • Additional reviewing methods for the estimation of unknown parameters, such as the method of percentiles, the method of moments, maximum likelihood inference, and Bayesian inference

Statistical Distributions, Fourth Edition is an excellent supplement for upper-undergraduate and graduate level courses on the topic. It is also a valuable reference for researchers and practitioners in the fields of engineering, economics, operations research, and the social sciences who conduct statistical analyses.

Product Details

ISBN-13:
9780470390634
Publisher:
Wiley
Publication date:
12/21/2010
Edition description:
New Edition
Pages:
230
Product dimensions:
6.10(w) x 9.20(h) x 0.70(d)

Related Subjects

Table of Contents

Prefacexv
1.Introduction1
2.Terms and Symbols3
2.1Probability, Random Variable, Variate, and Random Number3
2.2Range, Quantile, Probability Statements and Domain, and Distribution Function5
2.3Inverse Distribution and Survival Function8
2.4Probability Density Function and Probability Function9
2.5Other Associated Functions and Quantities11
3.General Variate Relationships17
3.1Introduction17
3.2Function of a Variate17
3.3One-to-One Transformations and Inverses18
3.4Variate Relationships Under One-to-One Transformation20
3.5Parameters, Variate, and Function Notation22
3.6Transformation of Location and Scale24
3.7Transformation from the Rectangular Variate25
3.8Many-to-One Transformations26
3.9Functions of Several Variates29
4.Bernoulli Distribution31
4.1Random Number Generation32
4.2Curtailed Bernoulli Trial Sequences32
4.3Urn Sampling Scheme33
4.4Note33
5.Beta Distribution34
5.1Notes on Beta and Gamma Functions35
5.2Variate Relationships37
5.3Parameter Estimation40
5.4Random Number Generation41
5.5Inverted Beta Distribution41
5.6Noncentral Beta Distribution42
5.7Beta Binomial Distribution42
6.Binomial Distribution43
6.1Variate Relationships44
6.2Parameter Estimation46
6.3Random Number Generation47
7.Cauchy Distribution48
7.1Note49
7.2Variate Relationships49
7.3Random Number Generation50
7.4Generalized Form50
8.Chi-Squared Distribution52
8.1Variate Relationships53
8.2Random Number Generation57
8.3Chi Distribution57
9.Chi-Squared (Noncentral) Distribution58
9.1Variate Relationships59
10.Dirichlet Distribution62
10.1Variate Relationships62
10.2Dirichlet Multinomial Distribution63
11.Empirical Distribution Function65
11.1Estimation from Uncensored Data65
11.2Estimation from Censored Data66
11.3Parameter Estimation67
11.4Example67
11.5Graphical Method for the Modified Order-Numbers69
11.6Model Accuracy70
12.Erlang Distribution71
12.1Variate Relationships72
12.2Parameter Estimation73
12.3Random Number Generation73
13.Error Distribution74
13.1Note75
13.2Variate Relationships76
14.Exponential Distribution77
14.1Note79
14.2Variate Relationships80
14.3Parameter Estimation81
14.4Random Number Generation81
15.Exponential Family82
15.1Members of the Exponential Family82
15.2Univariate One-Parameter Exponential Family82
15.3Estimation84
16.Extreme Value (Gumbel) Distribution85
16.1Note86
16.2Variate Relationships86
16.3Parameter Estimation89
16.4Random Number Generation89
17.F (Variance Ratio) or Fisher-Snedecor Distribution90
17.1Variate Relationships91
18.F (Noncentral) Distribution95
18.1Variate Relationships96
19.Gamma Distribution98
19.1Variate Relationships99
19.2Parameter Estimation101
19.3Random Number Generation102
19.4Inverted Gamma Distribution103
19.5Normal Gamma Distribution103
19.6Generalized Gamma Distribution104
20.Geometric Distribution106
20.1Notes107
20.2Variate Relationships108
20.3Random Number Generation108
21.Hypergeometric Distribution109
21.1Note111
21.2Variate Relationships111
21.3Parameter Estimation112
21.4Random Number Generation112
21.5Negative Hypergeometric Distribution112
21.6Generalized Hypergeometric (Series) Distribution113
22.Inverse Gaussian (Wald) Distribution114
22.1Variate Relationships115
22.2Parameter Estimation116
23.Laplace Distribution117
23.1Variate Relationships118
23.2Parameter Estimation120
23.3Random Number Generation120
24.Logarithmic Series Distribution121
24.1Variate Relationships122
24.2Parameter Estimation122
25.Logistic Distribution124
25.1Notes126
25.2Variate Relationships127
25.3Parameter Estimation128
25.4Random Number Generation128
26.Lognormal Distribution129
26.1Variate Relationships130
26.2Parameter Estimation133
26.3Random Number Generation133
27.Multinomial Distribution134
27.1Variate Relationships136
27.2Parameter Estimation136
28.Multivariate Normal (Multinormal) Distribution137
28.1Variate Relationships138
28.2Parameter Estimation139
29.Negative Binomial Distribution140
29.1Note142
29.2Variate Relationships142
29.3Parameter Estimation144
29.4Random Number Generation144
30.Normal (Gaussian) Distribution145
30.1Variate Relationships146
30.2Parameter Estimation150
30.3Random Number Generation150
31.Pareto Distribution151
31.1Note153
31.2Variate Relationships153
31.3Parameter Estimation154
31.4Random Number Generation154
32.Poisson Distribution155
32.1Note157
32.2Variate Relationships157
32.3Parameter Estimation160
32.4Random Number Generation160
33.Power Function Distribution161
33.1Variate Relationships162
33.2Parameter Estimation164
33.3Random Number Generation164
34.Power Series (Discrete) Distribution165
34.1Note166
34.2Variate Relationships166
33.3Parameter Estimation166
35.Rayleigh Distribution167
35.1Variate Relationships168
35.2Parameter Estimation169
36.Rectangular (Uniform) Continuous Distribution170
36.1Variate Relationships171
36.2Parameter Estimation174
36.3Random Number Generation174
37.Rectangular (Uniform) Discrete Distribution175
37.1General Form176
37.2Parameter Estimation177
38.Student's t Distribution178
38.1Variate Relationships180
38.2Random Number Generation183
39.Student's t (Noncentral) Distribution184
39.1Variate Relationships186
40.Triangular Distribution187
40.1Variate Relationships188
40.2Random Number Generation188
41.von Mises Distribution189
41.1Note190
41.2Variate Relationships191
41.3Parameter Estimation191
42.Weibull Distribution192
42.1Note193
42.2Variate Relationships194
42.3Parameter Estimation194
42.4Random Number Generation196
42.5Three-Parameter Weibull Distribution196
42.6Three-Parameter Weibull Random Number Generation197
42.7Bi-Weibull Distribution197
42.8Five-Parameter Bi-Weibull Distribution199
42.9Weibull Family202
43.Wishart (Central) Distribution204
43.1Note205
43.2Variate Relationships205
44.Computing References206
45.Statistical Tables210
45.1Normal Distribution Function211
45.2Percentiles of the Chi-Squared Distribution212
45.3Percentiles of the F Distribution214
45.4Percentiles of the Student's t Distribution218
45.5Partial Expectations for the Standard Normal Distribution219
Bibliography220

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