Univariate discrete distributions:
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| Previous Title: | Johnson, Norman Lloyd Discrete distributions |
|---|---|
| Main Authors: | , , |
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley
1992
|
| Edition: | 2. ed. |
| Series: | Wiley series in probability and mathematical statistics
A Wiley-interscience publication |
| Subjects: | |
| Online Access: | Publisher description Table of Contents Inhaltsverzeichnis |
| Item Description: | 1. Aufl. u.d.T.: Johnson, Norman L.: Discrete distributions |
| Physical Description: | XX, 565 S. |
| ISBN: | 0471548979 |
Staff View
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| 100 | 1 | |a Johnson, Norman L. |d 1939- |e Verfasser |0 (DE-588)137874383 |4 aut | |
| 245 | 1 | 0 | |a Univariate discrete distributions |c Norman L. Johnson ; Samuel Kotz ; Adrienne W. Kemp |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1992 | |
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| 500 | |a 1. Aufl. u.d.T.: Johnson, Norman L.: Discrete distributions | ||
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| 780 | 0 | 0 | |i Früher u.d.T. |a Johnson, Norman Lloyd |t Discrete distributions |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface xv
List of Tables xix
1 Preliminary Information 1
Introduction, 1
A Mathematical Preliminaries, 1
Al Factorial and Combinatorial Conventions, 1
A2 Gamma and Beta Functions, 4
A3 Finite Difference Calculus, 8
A4 Differential Calculus, 12
A5 Incomplete Gamma and Beta Functions, and Other Gamma
Related Functions, 14
A6 Gaussian Hypergeometric Functions, 17
A7 Confluent Hypergeometric Functions (Kummer s
Functions), 19
A8 Generalized Hypergeometric Functions, 22
A9 Bernoulli and Euler Numbers and Polynomials, 25
A10 Integral Transforms, 27
All Orthogonal Polynomials, 27
A12 Miscellaneous Topics, 29
B Probability and Statistical Preliminaries, 32
Bl Calculus of Probabilities, 32
B2 Real Variables, 35
B3 Bayes Theorem, 38
B4 Expected Values, 39
B5 Moments and Moment Generating Functions, 40
B6 Cumulants and Cumulant Generating Functions, 44
vii
Vlii CONTENTS
B7 Joint Moments and Cumulants, 46
B8 Characteristic Functions, 47
B9 Probability Generating Functions, 48
BIO Order Statistics, 51
Bll Truncation and Censoring, 52
B12 Mixture Distributions, 53
B13 Variance of a Function, 54
B14 Geometrical Concepts, 55
B15 Inference, 56
C Computer Generation of Univariate Discrete Random Variables, 61
Cl General Comments, 61
C2 Distributionally Non Specific Generation Procedures, 62
C3 Binomial Random Variables, 64
C4 Poisson Random Variables, 65
C5 Negative Binomial Random Variables, 66
C6 Hypergeometric Random Variables, 67
C7 Logarithmic Random Variables, 68
2 Families of Discrete Distributions 69
1 Lattice Distributions, 69
2 Power Series Distributions, 70
2.1 Generalized Power Series Distributions, 70
2.2 Modified Power Series Distributions, 74
3 Difference Equation Systems, 77
3.1 Katz and Extended Katz Families, 77
3.2 Ord s Family, 81
4 Kemp Families, 84
4.1 Generalized Hypergeometric Probability Distributions, 84
4.2 Generalized Hypergeometric Factorial Moment
Distributions, 91
5 Distributions Based on Lagrangian Expansions, 95
5.1 Otter s Multiplicative Process, 95
5.2 Lagrangian Distributions, 96
5.3 Gould and Abel Distributions, 100
6 Factorial Series Distributions, 102
3 Binomial Distribution 105
1 Definition, 105
2 Historical Remarks and Genesis, 106
CONTENTS ix
3 Moments, 106
4 Properties, 109
5 Order Statistics, 113
6 Approximations, Bounds, and Transformations, 114
6.1 Approximations, 114
6.2 Bounds, 120
6.3 Transformations, 122
7 Computation and Tables, 123
8 Estimation, 124
8.1 Model Selection, 124
8.2 Point Estimation, 125
8.3 Confidence Intervals, 129
8.4 Model Verification, 132
9 Characterizations, 133
10 Applications, 134
11 Truncated Binomial Distributions, 135
12 Other Related Distributions, 137
12.1 Limiting Forms, 137
12.2 Poissonian Binomial, Lexian, and Coolidge Schemes, 138
12.3 Binomial Binomial Lagrangian Distributions, 142
12.4 Weighted Binomial Distributions, 145
12.5 Pseudo Binomial Variables, 147
12.6 Correlated Binomial Variables, 148
4 Poisson Distribution 151
1 Definition, 151
2 Historical Remarks and Genesis, 151
3 Moments, 156
4 Properties, 158
5 Approximations, Bounds, and Transformations, 162
6 Computation and Tables, 165
7 Estimation, 166
7.1 Model Selection, 166
7.2 Point Estimation, 168
7.3 Confidence Intervals, 170
7.4 Model Verification, 172
8 Characterizations, 173
9 Applications, 179
10 Truncated and Misrecorded Poisson Distributions, 181
x CONTENTS
10.1 Left Truncation, 181
10.2 Right Truncation and Double Truncation, 184
10.3 Misrecorded Poisson Distributions, 186
11 Poisson Stopped Sum Distributions, 188
12 Other Related Distributions, 189
12.1 The Normal Distribution, 189
12.2 The Gamma Distribution, 189
12.3 Sums and Differences of Poisson Variates, 190
12.4 Hyper Poisson Distributions, 192
12.5 Grouped Poisson Distributions, 195
12.6 Heine and Euler Distributions, 197
5 Negative Binomial Distribution 199
1 Definition, 199
2 Geometric Distribution, 201
3 Historical Remarks and Genesis, 203
4 Moments, 207
5 Properties, 208
6 Approximations and Transformations, 209
7 Computation and Tables, 213
8 Estimation, 214
8.1 Model Selection, 214
8.2 P Unknown, 215
8.3 Both Parameters Unknown, 216
8.4 Data Sets with a Common Parameter, 219
9 Characterizations, 220
9.1 Geometric Distribution, 220
9.2 Negative Binomial Distribution, 223
10 Applications, 223
11 Truncated Negative Binomial Distributions, 225
12 Other Related Distributions, 228
12.1 Limiting Forms, 228
12.2 Engen s Extended Negative Binomial Model, 229
12.3 Lagrangian Generalized Negative Binomial
Distribution , 230
12.4 Weighted Negative Binomial Distributions, 230
12.5 Convolutions Involving Negative Binomial Variates, 231
12.6 Pascal Poisson Distribution, 233
12.7 A Riff Shuffle Distribution, 234
CONTENTS Xi
6 Hypergeometric Distributions 237
1 Definition, 237
2 Historical Remarks and Genesis, 238
2.1 Classical Hypergeometric Distribution, 238
2.2 Negative (Inverse) Hypergeometric Distribution:
Hypergeometric Waiting Time Distribution, Beta Binomial
Distribution, 239
2.3 Beta Negative Binomial Distribution: Beta Pascal
Distribution, Generalized Waring Distribution, 242
2.4 Polya Distributions: Generalized Hypergeometric
Distributions, 244
3 Moments, 249
4 Properties, 253
5 Approximations and Bounds, 256
6 Tables and Computation, 262
7 Estimation, 262
7.1 Classical Hypergeometric Distribution, 262
7.2 Negative (Inverse) Hypergeometric Distribution, 264
7.3 Beta Pascal Distribution, 266
8 Characterizations, 266
9 Applications, 269
9.1 Classical Hypergeometric Distribution, 269
9.2 Negative (Inverse) Hypergeometric Distribution:
Beta Binomial Distribution, 270
9.3 Beta Negative Binomial Distribution: Beta Pascal
Distribution, Generalized Waring Distribution, 271
10 Special Cases, 272
10.1 Discrete Rectangular Distribution, 272
10.2 Distribution of Leads in Coin Tossing, 274
10.3 Yule Distribution, 275
10.4 Waring Distribution, 278
11 Extended Hypergeometric Distributions, 279
12 Other Related Distributions, 282
7 Logarithmic Distribution 285
1 Definition, 285
2 Historical Remarks and Genesis, 286
3 Moments, 288
4 Properties, 290
Xli CONTENTS
5 Approximations and Bounds, 291
6 Computation and Tables, 292
7 Estimation, 293
7.1 Model Selection, 293
7.2 Point Estimation and Confidence Intervals, 294
8 Characterizations, 297
9 Applications, 298
10 Truncated and Modified Logarithmic Distributions, 299
11 Other Related Distributions, 300
8 Mixture Distributions 305
1 Introduction, 305
2 Finite Mixtures of Discrete Distributions, 309
2.1 Parameters of Finite Mixtures, 309
2.2 Zero Modified Distributions, 312
2.3 Finite Poisson Mixtures, 318
2.4 Finite Binomial Mixtures, 319
2.5 Other Finite Mixtures of Discrete Distributions, 321
3 Continuous and Countable Mixtures of Discrete Distributions, 322
3.1 Three Important Theorems, 322
3.2 Mixtures of Poisson Distributions, 326
3.3 Mixtures of Binomial Distributions, 335
3.4 Other Continuous and Countable Mixtures of Discrete
Distributions, 337
9 Generalized (Stopped Sum) Distributions 343
1 Introduction, 343
2 Damage Processes, 349
3 Poisson Stopped Sum Distributions: Generalized Poisson
Distributions, 351
4 Hermite Distribution, 357
5 Poisson Binomial Distribution, 364
6 Neyman Type A Distribution, 368
6.1 Definition, 368
6.2 Moment Properties, 371
6.3 Tables and Approximations, 372
6.4 Estimation, 374
6.5 Applications, 376
7 Polya Aeppli Distribution, 378
CONTENTS Xiii
8 Poisson Pascal Distribution: Poisson Negative Binomial
Distribution, Generalized Polya Aeppli Distribution, 382
9 Generalizations of the Neyman Type A Distribution, 386
10 Thomas Distribution, 392
11 Lagrangian Poisson Distribution: Shifted Borel Tanner
Distribution, 394
12 Other Families of Stopped Sum Distributions, 400
10 Matching, Occupancy, and Runs Distributions 405
1 Introduction, 405
2 Probabilities of Combined Events, 406
3 Matching Distributions, 409
4 Occupancy Distributions, 414
4.1 Classical Occupancy and Coupon Collecting, 414
4.2 Maxwell Boltzmann, Bose Einstein, and Fermi Dirac
Statistics, 420
5 Runs Distributions, 422
5.1 Runs of Like Elements, 422
5.2 Runs Up and Down, 425
6 Distributions of Order k, 426
6.1 Success Runs Distributions, 426
6.2 Philippou, Aki, and Hirano s Distributions of Order k, 427
6.3 Further Distributions of Order k, 432
11 Miscellaneous Discrete Distributions 433
1 Absorption Distribution, 433
2 Dandekar s Modified Binomial and Poisson Distributions, 435
3 Digamma and Trigamma Distributions, 436
4 Discrete Ades Distribution, 437
5 Discrete Student s f Distribution, 438
6 Geeta Distribution, 439
7 Gegenbauer Distribution: Negative Binomial*Pseudo Negative
Binomial Convolution, 440
8 Gram Charlier Type B Distributions, 442
9 Interrupted Distributions, 443
10 Lost Games Distributions, 445
11 Naor s Distribution, 447
12 Partial Sums Distributions, 448
13 Queueing Theory Distributions, 451
XIV CONTENTS
14 Record Value Distributions, 453
15 Sichel Distribution: Poisson Inverse Gaussian Distribution, 455
16 Skellam s Gene Frequency Distribution, 457
17 Steyn s Two Parameter Power Series Distributions, 459
18 Univariate Multinomial Type Distributions, 460
19 Urn Models with Stochastic Replacements, 463
20 Zipf and Zeta Distributions, 465
Bibliography 473
Abbreviations 549
Index 551
|
| any_adam_object | 1 |
| author | Johnson, Norman L. 1939- Kotz, Samuel 1930-2010 Kemp, Adrienne W. |
| author_GND | (DE-588)137874383 (DE-588)119529653 (DE-588)170584763 |
| author_facet | Johnson, Norman L. 1939- Kotz, Samuel 1930-2010 Kemp, Adrienne W. |
| author_role | aut aut aut |
| author_sort | Johnson, Norman L. 1939- |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra 519 - Probabilities and applied mathematics |
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| dewey-search | 512.2/4 519.24 |
| dewey-sort | 3512.2 14 |
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| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV007100080 |
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| indexdate | 2024-07-09T16:55:32Z |
| institution | BVB |
| isbn | 0471548979 |
| language | English |
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| physical | XX, 565 S. |
| publishDate | 1992 |
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| publisher | Wiley |
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| series2 | Wiley series in probability and mathematical statistics A Wiley-interscience publication |
| spelling | Johnson, Norman L. 1939- Verfasser (DE-588)137874383 aut Univariate discrete distributions Norman L. Johnson ; Samuel Kotz ; Adrienne W. Kemp 2. ed. New York [u.a.] Wiley 1992 XX, 565 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and mathematical statistics A Wiley-interscience publication 1. Aufl. u.d.T.: Johnson, Norman L.: Discrete distributions Distribution (Théorie des probabilités) Distribution (Théorie des probabilités) - Bibliographie Verdelingen (statistiek) gtt Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd rswk-swf Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 s DE-604 Kotz, Samuel 1930-2010 Verfasser (DE-588)119529653 aut Kemp, Adrienne W. Verfasser (DE-588)170584763 aut Früher u.d.T. Johnson, Norman Lloyd Discrete distributions http://www.loc.gov/catdir/description/wiley031/92011685.html Publisher description http://www.loc.gov/catdir/toc/onix01/92011685.html Table of Contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004518815&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Johnson, Norman L. 1939- Kotz, Samuel 1930-2010 Kemp, Adrienne W. Univariate discrete distributions Distribution (Théorie des probabilités) Distribution (Théorie des probabilités) - Bibliographie Verdelingen (statistiek) gtt Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd |
| subject_GND | (DE-588)4150184-6 |
| title | Univariate discrete distributions |
| title_auth | Univariate discrete distributions |
| title_exact_search | Univariate discrete distributions |
| title_full | Univariate discrete distributions Norman L. Johnson ; Samuel Kotz ; Adrienne W. Kemp |
| title_fullStr | Univariate discrete distributions Norman L. Johnson ; Samuel Kotz ; Adrienne W. Kemp |
| title_full_unstemmed | Univariate discrete distributions Norman L. Johnson ; Samuel Kotz ; Adrienne W. Kemp |
| title_old | Johnson, Norman Lloyd Discrete distributions |
| title_short | Univariate discrete distributions |
| title_sort | univariate discrete distributions |
| topic | Distribution (Théorie des probabilités) Distribution (Théorie des probabilités) - Bibliographie Verdelingen (statistiek) gtt Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd |
| topic_facet | Distribution (Théorie des probabilités) Distribution (Théorie des probabilités) - Bibliographie Verdelingen (statistiek) Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung |
| url | http://www.loc.gov/catdir/description/wiley031/92011685.html http://www.loc.gov/catdir/toc/onix01/92011685.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=004518815&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT johnsonnormanl univariatediscretedistributions AT kotzsamuel univariatediscretedistributions AT kempadriennew univariatediscretedistributions |