Univariate discrete distributions:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ [u.a.]
Wiley-Interscience
2005
|
| Edition: | 3. ed. |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Table of contents only Contributor biographical information Publisher description Inhaltsverzeichnis Klappentext |
| Item Description: | 1st. ed. u.d.T.: Discrete distributions Includes bibliographical references (p. 535-630) and index |
| Physical Description: | XIX, 646 S. 24 cm |
| ISBN: | 0471272469 9780471272465 |
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| 084 | |a MAT 603f |2 stub | ||
| 100 | 1 | |a Johnson, Norman Lloyd |d 1917-2004 |e Verfasser |0 (DE-588)128650419 |4 aut | |
| 245 | 1 | 0 | |a Univariate discrete distributions |c Norman L. Johnson ; Adrienne W. Kemp ; Samuel Kotz |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Hoboken, NJ [u.a.] |b Wiley-Interscience |c 2005 | |
| 300 | |a XIX, 646 S. |c 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 500 | |a 1st. ed. u.d.T.: Discrete distributions | ||
| 500 | |a Includes bibliographical references (p. 535-630) and index | ||
| 650 | 4 | |a Distribution (Théorie des probabilités) | |
| 650 | 7 | |a Univariate methoden |2 gtt | |
| 650 | 7 | |a Verdelingen (statistiek) |2 gtt | |
| 650 | 4 | |a Distribution (Probability theory) | |
| 650 | 0 | 7 | |a Diskrete Wahrscheinlichkeitsverteilung |0 (DE-588)4150184-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Diskrete Wahrscheinlichkeitsverteilung |0 (DE-588)4150184-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Kemp, Adrienne W. |e Verfasser |4 aut | |
| 700 | 1 | |a Kotz, Samuel |d 1930-2010 |e Verfasser |0 (DE-588)119529653 |4 aut | |
| 856 | 4 | |u http://www.loc.gov/catdir/toc/ecip0515/2005019970.html |3 Table of contents only | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0622/2005019970-b.html |3 Contributor biographical information | |
| 856 | 4 | |u http://www.loc.gov/catdir/enhancements/fy0622/2005019970-d.html |3 Publisher description | |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016277563&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 856 | 4 | 2 | |m Digitalisierung UB Passau |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016277563&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |3 Klappentext |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-016277563 | ||
Record in the Search Index
| _version_ | 1804137319283818496 |
|---|---|
| adam_text | Contents
Preface
xvii
1
Preliminary
Information
1
1.1
Mathematical Preliminaries,
1
1.1.1
Factorial and Combinatorial Conventions,
1
1.1.2
Gamma and Beta Functions,
5
1.1.3
Finite Difference Calculus,
10
1.1.4
Differential Calculus,
14
1.1.5
Incomplete Gamma and Beta Functions and Other
Gamma-Related Functions,
16
1.1.6
Gaussian Hypergeometric Functions,
20
1.1.7
Confluent Hypergeometric Functions
(Kummer
s
Functions),
23
1.1.8
Generalized Hypergeometric Functions,
26
1.1.9
Bernoulli and
Euler
Numbers and Polynomials,
29
1.1.10
Integral Transforms,
32
1.1.11
Orthogonal Polynomials,
32
1.1.12
Basic Hypergeometric Series,
34
1.2
Probability and Statistical Preliminaries,
37
1.2.1
Calculus of Probabilities,
37
1.2.2
Bayes s
Theorem,
41
1.2.3
Random Variables,
43
1.2.4
Survival Concepts,
45
1.2.5
Expected Values,
47
1.2.6
Inequalities,
49
1.2.7
Moments and Moment Generating Functions,
50
1.2.8
Cumulants
and
Cumulant
Generating Functions,
54
Vlil
CONTENTS
1.2.9 Joint Moments and
Cumulants,
56
1.2.10 Characteristic
Functions,
57
1.2.11
Probability Generating Functions,
58
1.2.12 Order
Statistics,
61
1.2.13
Truncation and Censoring,
62
1.2.14
Mixture Distributions,
64
1.2.15
Variance of a Function,
65
1.2.16
Estimation,
66
1.2.17
General Comments on the Computer Generation of
Discrete Random Variables,
71
1.2.18
Computer Software,
73
2
Families of Discrete Distributions
74
2.1
Lattice Distributions,
74
2.2
Power Series Distributions,
75
2.2.1
Generalized Power Series Distributions,
75
2.2.2
Modified Power Series Distributions,
79
2.3
Difference-Equation Systems,
82
2.3.1
Katz and Extended Katz Families,
82
2.3.2
Sundt and Jewell Family,
85
2.3.3
Orďs
Family,
87
2.4
Kemp Families,
89
2.4.1
Generalized Hypergeometrie Probability
Distributions,
89
2.4.2
Generalized Hypergeometrie Factorial Moment
Distributions,
96
2.5
Distributions Based on Lagrangian Expansions,
99
2.6
Gould and Abel Distributions,
101
2.7
Factorial Series Distributions,
103
2.8
Distributions of Order-A;,
105
2.9 <?
-Series Distributions,
106
3
Binomial Distribution
108
3.1
Definition,
108
3.2
Historical Remarks and Genesis,
109
3.3
Moments,
109
3.4
Properties,
112
3.5
Order Statistics,
116
3.6
Approximations, Bounds, and Transformations,
116
CONTENTS
IX
3.6.1
Approximations,
116
3.6.2
Bounds,
122
3.6.3
Transformations,
123
3.7
Computation,
Tables, and Computer
Generation,
124
3.7.1
Computation and Tables,
124
3.7.2
Computer Generation,
125
3.8
Estimation,
126
3.8.1
Model Selection,
126
3.8.2
Point Estimation,
126
3.8.3
Confidence Intervals,
130
3.8.4
Model Verification,
133
3.9
Characterizations,
134
3.10
Applications,
135
3.11
Truncated Binomial Distributions,
137
3.12
Other Related Distributions,
140
3.12.1
Limiting Forms,
140
3.12.2
Sums and Differences of Binomial-Type
Variables,
140
3.12.3
Poissonian Binomial, Lexian, and Coolidge
Schemes,
144
3.12.4
Weighted Binomial Distributions,
149
3.12.5
Chain Binomial Models,
151
3.12.6
Correlated Binomial Variables,
151
4
Poisson
Distribution
156
4.1
Definition,
156
4.2
Historical Remarks and Genesis,
156
4.2.1
Genesis,
156
4.2.2
Poissonian Approximations,
160
4.3
Moments,
161
4.4
Properties,
163
4.5
Approximations, Bounds, and Transformations,
167
4.6
Computation, Tables, and Computer Generation,
170
4.6.1
Computation and Tables,
170
4.6.2
Computer
Generation, 171
4.7
Estimation,
173
4.7.1
Model Selection,
173
4.7.2
Point Estimation,
174
4.7.3
Confidence Intervals,
176
4.7.4
Model
Verification,
178
4.8
Characterizations,
179
4.9
Applications,
186
4.10
Truncated and Misrecorded
Poisson
Distributions,
188
4.10.1
Left Truncation,
188
4.10.2
Right Truncation and Double Truncation,
191
4.10.3
Misrecorded
Poisson
Distributions,
193
4.11
Poisson-Stopped Sum Distributions,
195
4.12
Other Related Distributions,
196
4.12.1
Normal Distribution,
196
4.12.2
Gamma Distribution,
196
4.12.3
Sums and Differences of
Poisson Variâtes,
197
4.12.4
Hyper-Poisson
Distributions,
199
4.12.5
Grouped
Poisson
Distributions,
202
4.12.6
Heine and
Euler
Distributions,
205
4.12.7
Intervened
Poisson
Distributions,
205
Negative Binomial Distribution
208
5.1
Definition,
208
5.2
Geometric Distribution,
210
5.3
Historical Remarks and Genesis of Negative Binomial
Distribution,
212
5.4
Moments,
215
5.5
Properties,
217
5.6
Approximations and Transformations,
218
5.7
Computation and Tables,
220
5.8
Estimation,
222
5.8.1
Model Selection,
222
5.8.2
Ρ
Unknown,
222
5.8.3
Both Parameters Unknown,
223
5.8.4
Data Sets with a Common Parameter,
226
5.8.5
Recent Developments,
227
5.9
Characterizations,
228
5.9.1
Geometric Distribution,
228
5.9.2
Negative Binomial Distribution,
231
5.10
Applications,
232
5.11
Truncated Negative Binomial Distributions,
233
5.12
Related Distributions,
236
5.12.1
Limiting Forms,
236
5.12.2
Extended Negative Binomial Model,
237
5.12.3
Lagrangian Generalized Negative Binomial
Distribution,
239
5.12.4
Weighted Negative Binomial Distributions,
240
5.12.5
Convolutions Involving Negative Binomial
Variâtes,
241
5.12.6
Pascal-Poisson
Distribution,
243
5.12.7
Minimum (Riff-Shuffle) and Maximum Negative
Binomial Distributions,
244
5.12.8
Condensed Negative Binomial Distributions,
246
5.12.9
Other Related Distributions,
247
6
Hypergeometric Distributions
6.1
Definition,
251
6.2
Historical Remarks and Genesis,
252
6.2.1
Classical Hypergeometric Distribution,
252
6.2.2
Beta-Binomial Distribution, Negative (Inverse)
Hypergeometric Distribution: Hypergeometric
Waiting-Time Distribution,
253
6.2.3
Beta-Negative Binomial Distribution: Beta-Pascal
Distribution, Generalized Waring Distribution,
256
6.2.4
Pólya
Distributions,
258
6.2.5
Hypergeometric Distributions in General,
259
6.3
Moments,
262
6.4
Properties,
265
6.5
Approximations and Bounds,
268
6.6
Tables, Computation, and Computer Generation,
271
6.7
Estimation,
272
6.7.1
Classical Hypergeometric Distribution,
273
6.7.2
Negative (Inverse) Hypergeometric Distribution:
Beta-Binomial Distribution,
274
6.7.3
Beta-Pascal Distribution,
276
6.8
Characterizations,
277
6.9
Applications,
279
6.9.1
Classical Hypergeometric Distribution,
279
6.9.2
Negative (Inverse) Hypergeometric Distribution:
Beta-Binomial Distribution,
281
6.9.3
Beta-Negative Binomial Distribution: Beta-Pascal
Distribution, Generalized Waring Distribution,
283
6.10
Special Cases,
283
6.10.1
Discrete
Rectangular
Distribution, 283
6.10.2 Distribution
of Leads in Coin Tossing,
286
6.10.3
Yule Distribution,
287
6.10.4
Waring Distribution,
289
6.10.5
Narayana Distribution,
291
6.11
Related Distributions,
293
6.11.1
Extended Hypergeometric Distributions,
293
6.11.2
Generalized Hypergeometric Probability
Distributions,
296
6.11.3
Generalized Hypergeometric Factorial Moment
Distributions,
298
6.11.4
Other Related Distributions,
299
7
Logarithmic and Lagrangian Distributions
302
7.1
Logarithmic Distribution,
302
7.1.1
Definition,
302
7.1.2
Historical Remarks and Genesis,
303
7.1.3
Moments,
305
7.1.4
Properties,
307
7.1.5
Approximations and Bounds,
309
7.1.6
Computation, Tables, and Computer
Generation,
310
7.1.7
Estimation,
311
7.1.8
Characterizations,
315
7.1.9
Applications,
316
7.1.10
Truncated and Modified Logarithmic
Distributions,
317
7.1.11
Generalizations of the Logarithmic Distribution,
319
7.1.12
Other Related Distributions,
321
7.2
Lagrangian Distributions,
325
7.2.1
Otter s Multiplicative Process,
326
7.2.2
Borei
Distribution,
328
7.2.3
Consul Distribution,
329
7.2.4
Geeta Distribution,
330
7.2.5
General Lagrangian Distributions of the First
Kind,
331
7.2.6
Lagrangian
Poisson
Distribution,
336
7.2.7
Lagrangian Negative Binomial Distribution,
340
7.2.8
Lagrangian Logarithmic Distribution,
341
7.2.9
Lagrangian Distributions of the Second Kind,
342
і
Mixture Distributions
343
8.1
Basic Ideas,
343
8.1.1
Introduction,
343
8.1.2
Finite Mixtures,
344
8.1.3
Varying Parameters,
345
8.1.4
Bayesian Interpretation,
347
8.2
Finite Mixtures of Discrete Distributions,
347
8.2.1
Parameters of Finite Mixtures,
347
8.2.2
Parameter Estimation,
349
8.2.3
Zero-Modified and Hurdle Distributions,
351
8.2.4
Examples of Zero-Modified Distributions,
353
8.2.5
Finite
Poisson
Mixtures,
357
8.2.6
Finite Binomial Mixtures,
358
8.2.7
Other Finite Mixtures of Discrete Distributions,
359
8.3
Continuous and Countable Mixtures of Discrete
Distributions,
360
8.3.1
Properties of General Mixed Distributions,
360
8.3.2
Properties of Mixed
Poisson
Distributions,
362
8.3.3
Examples of
Poisson
Mixtures,
365
8.3.4
Mixtures of Binomial Distributions,
373
8.3.5
Examples of Binomial Mixtures,
374
8.3.6
Other Continuous and Countable Mixtures of
Discrete Distributions,
376
8.4
Gamma and Beta Mixing Distributions,
378
9
Stopped-Sum Distributions
381
9.1
Generalized and Generalizing Distributions,
381
9.2
Damage Processes,
386
9.3
Poisson-
Stopped Sum (Multiple
Poisson)
Distributions,
388
9.4
Hermite Distribution,
394
9.5
Poisson-Binomial Distribution,
400
9.6
Neyman Type A Distribution,
403
9.6.1
Definition,
403
9.6.2
Moment Properties,
405
9.6.3
Tables and Approximations,
406
9.6.4
Estimation,
407
9.6.5
Applications,
409
9.7
Pólya-Aeppli
Distribution,
410
9.8
Generalized
Pólya-Aeppli
(Poisson-Négative
Binomial)
Distribution,
414
9.9
Generalizations of Neyman Type A Distribution,
416
9.10
Thomas Distribution,
421
9.11
Borel-Tanner Distribution: Lagrangian
Poisson
Distribution,
423
9.12
Other Poisson-Stopped Sum (multiple
Poisson)
Distributions,
425
9.13
Other Families of Stopped-Sum Distributions,
426
10
Matching, Occupancy, Runs, and
q
-Series Distributions
430
10.1
Introduction,
430
10.2
Probabilities of Combined Events,
431
10.3
Matching Distributions,
434
10.4
Occupancy Distributions,
439
10.4.1
Classical Occupancy and Coupon Collecting,
439
10.4.2
Maxwell-
В
oltzmann, Bose-Einstein, and
Fermi-Dirac Statistics,
444
10.4.3
Specified Occupancy and Grassia-Binomial
Distributions,
446
10.5
Record Value Distributions,
448
10.6
Runs Distributions,
450
10.6.1
Runs of Like Elements,
450
10.6.2
Runs Up and Down,
453
10.7
Distributions of Order k,
454
10.7.1
Early Work on Success Runs Distributions,
454
10.7.2
Geometric Distribution of Order k,
456
10.7.3
Negative Binomial Distributions of Order k,
458
10.7.4
Poisson
and Logarithmic Distributions of
Order k,
459
10.7.5
Binomial Distributions of Order k,
461
10.7.6
Further Distributions of Order k,
463
10.8
^-Series Distributions,
464
10.8.1
Terminating Distributions,
465
10.8.2
g-Series Distributions with Infinite Support,
470
10.8.3
Bilateral ^-Series Distributions,
474
10.8.4
^-Series Related Distributions,
476
11
Parametric
Regression Models
and Miscellanea
478
11.1
Parametric Regression Models,
478
11.1.1
Introduction,
478
11.1.2
Tweedie-Poisson Family,
480
11.1.3
Negative Binomial Regression Models,
482
11.1.4
Poisson
Lognormal
Model,
483
11.1.5
Poisson-Inverse
Gaussian
(Sichel)
Model,
484
11.1.6
Poisson
Polynomial Distribution,
487
11.1.7
Weighted
Poisson
Distributions,
488
11.1.8
Double-Poisson
and Double-Binomial
Distributions,
489
11.1.9
Simplex-Binomial Mixture Model,
490
11.2
Miscellaneous Discrete Distributions,
491
11.2.1
Dandekar s Modified Binomial and
Poisson
Models,
491
11.2.2
Digamma
and Trigamma Distributions,
492
11.2.3
Discrete
Adès
Distribution,
494
11.2.4
Discrete Bessel Distribution,
495
11.2.5
Discrete
Mittag
-Leffler Distribution,
496
11.2.6
Discrete Student s
t
Distribution,
498
11.2.7
Feller-Arley and
Gegenbauer
Distributions,
499
11.2.8
Gram-Charlier Type
В
Distributions,
501
11.2.9
Interrupted Distributions,
502
11.2.10
Lost-Games Distributions,
503
11.2.11
Luria-Delbriick Distribution,
505
11.2.12
Naor
s
Distribution,
507
11.2.13
Partial-Sums Distributions,
508
11.2.14
Queueing Theory Distributions,
512
11.2.15
Reliability and Survival Distributions,
514
11.2.16
Skellam-Haldane Gene Frequency Distribution,
519
11.2.17
Steyn s Two-Parameter Power Series
Distributions,
521
11.2.18
Univariate Multinomial-Type Distributions,
522
11.2.19
Urn Models with Stochastic Replacements,
524
11.2.20
Zipf-Related Distributions,
526
11.2.21
Haighť s
Zeta
Distributions,
533
Bibliography
Abbreviations
Index
535
631
633
The Third Edition of the critically acclaimed Univariate Discrete Distributions provides
a self-contained, systematic treatment of the theory, derivation, and application of
probability distributions for count data. Generalized zeta-function and q-series
distributions have been added and are covered in detail. New families of distributions,
including Lagrangian-type distributions, are integrated into this thoroughly revised
and updated text. Additional applications of univariate discrete distributions are
explored to demonstrate the flexibility of this powerful method.
A thorough survey of recent statistical literature draws attention to many
new distributions and results for the classical distributions. Approximately
450
new
references along with several new sections are introduced to reflect the current
literature and knowledge of discrete distributions.
Beginning with mathematical, probability, and statistical fundamentals, the authors
provide clear coverage of the key topics in the field, including:
•
Families of discrete distributions
•
Binomial distribution
•
Poisson
distribution
•
Negative binomial distribution
•
Hypergeometric distributions
•
Logarithmic and Lagranglan distributions
•
Mixture distributions
•
Stopped-sum distributions
•
Matching, occupancy, runs, and q-series distributions
•
Parametric regression models and miscellanea
Emphasis continues to be placed on the increasing relevance of Bayesian inference to
discrete distribution, especially with regard to the binomial and
Poisson
distributions.
New derivations of discrete distributions via stochastic processes and random walks
are introduced without unnecessarily complex discussions of stochastic processes.
Throughout the Third Edition, extensive information has been added to reflect the new
role of computer-based applications.
With Its thorough coverage and balanced presentation of theory and application, this
is an excellent and essential reference for statisticians and mathematicians.
|
| adam_txt |
Contents
Preface
xvii
1
Preliminary
Information
1
1.1
Mathematical Preliminaries,
1
1.1.1
Factorial and Combinatorial Conventions,
1
1.1.2
Gamma and Beta Functions,
5
1.1.3
Finite Difference Calculus,
10
1.1.4
Differential Calculus,
14
1.1.5
Incomplete Gamma and Beta Functions and Other
Gamma-Related Functions,
16
1.1.6
Gaussian Hypergeometric Functions,
20
1.1.7
Confluent Hypergeometric Functions
(Kummer'
s
Functions),
23
1.1.8
Generalized Hypergeometric Functions,
26
1.1.9
Bernoulli and
Euler
Numbers and Polynomials,
29
1.1.10
Integral Transforms,
32
1.1.11
Orthogonal Polynomials,
32
1.1.12
Basic Hypergeometric Series,
34
1.2
Probability and Statistical Preliminaries,
37
1.2.1
Calculus of Probabilities,
37
1.2.2
Bayes's
Theorem,
41
1.2.3
Random Variables,
43
1.2.4
Survival Concepts,
45
1.2.5
Expected Values,
47
1.2.6
Inequalities,
49
1.2.7
Moments and Moment Generating Functions,
50
1.2.8
Cumulants
and
Cumulant
Generating Functions,
54
Vlil
CONTENTS
1.2.9 Joint Moments and
Cumulants,
56
1.2.10 Characteristic
Functions,
57
1.2.11
Probability Generating Functions,
58
1.2.12 Order
Statistics,
61
1.2.13
Truncation and Censoring,
62
1.2.14
Mixture Distributions,
64
1.2.15
Variance of a Function,
65
1.2.16
Estimation,
66
1.2.17
General Comments on the Computer Generation of
Discrete Random Variables,
71
1.2.18
Computer Software,
73
2
Families of Discrete Distributions
74
2.1
Lattice Distributions,
74
2.2
Power Series Distributions,
75
2.2.1
Generalized Power Series Distributions,
75
2.2.2
Modified Power Series Distributions,
79
2.3
Difference-Equation Systems,
82
2.3.1
Katz and Extended Katz Families,
82
2.3.2
Sundt and Jewell Family,
85
2.3.3
Orďs
Family,
87
2.4
Kemp Families,
89
2.4.1
Generalized Hypergeometrie Probability
Distributions,
89
2.4.2
Generalized Hypergeometrie Factorial Moment
Distributions,
96
2.5
Distributions Based on Lagrangian Expansions,
99
2.6
Gould and Abel Distributions,
101
2.7
Factorial Series Distributions,
103
2.8
Distributions of Order-A;,
105
2.9 <?
-Series Distributions,
106
3
Binomial Distribution
108
3.1
Definition,
108
3.2
Historical Remarks and Genesis,
109
3.3
Moments,
109
3.4
Properties,
112
3.5
Order Statistics,
116
3.6
Approximations, Bounds, and Transformations,
116
CONTENTS
IX
3.6.1
Approximations,
116
3.6.2
Bounds,
122
3.6.3
Transformations,
123
3.7
Computation,
Tables, and Computer
Generation,
124
3.7.1
Computation and Tables,
124
3.7.2
Computer Generation,
125
3.8
Estimation,
126
3.8.1
Model Selection,
126
3.8.2
Point Estimation,
126
3.8.3
Confidence Intervals,
130
3.8.4
Model Verification,
133
3.9
Characterizations,
134
3.10
Applications,
135
3.11
Truncated Binomial Distributions,
137
3.12
Other Related Distributions,
140
3.12.1
Limiting Forms,
140
3.12.2
Sums and Differences of Binomial-Type
Variables,
140
3.12.3
Poissonian Binomial, Lexian, and Coolidge
Schemes,
144
3.12.4
Weighted Binomial Distributions,
149
3.12.5
Chain Binomial Models,
151
3.12.6
Correlated Binomial Variables,
151
4
Poisson
Distribution
156
4.1
Definition,
156
4.2
Historical Remarks and Genesis,
156
4.2.1
Genesis,
156
4.2.2
Poissonian Approximations,
160
4.3
Moments,
161
4.4
Properties,
163
4.5
Approximations, Bounds, and Transformations,
167
4.6
Computation, Tables, and Computer Generation,
170
4.6.1
Computation and Tables,
170
4.6.2
Computer
Generation, 171
4.7
Estimation,
173
4.7.1
Model Selection,
173
4.7.2
Point Estimation,
174
4.7.3
Confidence Intervals,
176
4.7.4
Model
Verification,
178
4.8
Characterizations,
179
4.9
Applications,
186
4.10
Truncated and Misrecorded
Poisson
Distributions,
188
4.10.1
Left Truncation,
188
4.10.2
Right Truncation and Double Truncation,
191
4.10.3
Misrecorded
Poisson
Distributions,
193
4.11
Poisson-Stopped Sum Distributions,
195
4.12
Other Related Distributions,
196
4.12.1
Normal Distribution,
196
4.12.2
Gamma Distribution,
196
4.12.3
Sums and Differences of
Poisson Variâtes,
197
4.12.4
Hyper-Poisson
Distributions,
199
4.12.5
Grouped
Poisson
Distributions,
202
4.12.6
Heine and
Euler
Distributions,
205
4.12.7
Intervened
Poisson
Distributions,
205
Negative Binomial Distribution
208
5.1
Definition,
208
5.2
Geometric Distribution,
210
5.3
Historical Remarks and Genesis of Negative Binomial
Distribution,
212
5.4
Moments,
215
5.5
Properties,
217
5.6
Approximations and Transformations,
218
5.7
Computation and Tables,
220
5.8
Estimation,
222
5.8.1
Model Selection,
222
5.8.2
Ρ
Unknown,
222
5.8.3
Both Parameters Unknown,
223
5.8.4
Data Sets with a Common Parameter,
226
5.8.5
Recent Developments,
227
5.9
Characterizations,
228
5.9.1
Geometric Distribution,
228
5.9.2
Negative Binomial Distribution,
231
5.10
Applications,
232
5.11
Truncated Negative Binomial Distributions,
233
5.12
Related Distributions,
236
5.12.1
Limiting Forms,
236
5.12.2
Extended Negative Binomial Model,
237
5.12.3
Lagrangian Generalized Negative Binomial
Distribution,
239
5.12.4
Weighted Negative Binomial Distributions,
240
5.12.5
Convolutions Involving Negative Binomial
Variâtes,
241
5.12.6
Pascal-Poisson
Distribution,
243
5.12.7
Minimum (Riff-Shuffle) and Maximum Negative
Binomial Distributions,
244
5.12.8
Condensed Negative Binomial Distributions,
246
5.12.9
Other Related Distributions,
247
6
Hypergeometric Distributions
6.1
Definition,
251
6.2
Historical Remarks and Genesis,
252
6.2.1
Classical Hypergeometric Distribution,
252
6.2.2
Beta-Binomial Distribution, Negative (Inverse)
Hypergeometric Distribution: Hypergeometric
Waiting-Time Distribution,
253
6.2.3
Beta-Negative Binomial Distribution: Beta-Pascal
Distribution, Generalized Waring Distribution,
256
6.2.4
Pólya
Distributions,
258
6.2.5
Hypergeometric Distributions in General,
259
6.3
Moments,
262
6.4
Properties,
265
6.5
Approximations and Bounds,
268
6.6
Tables, Computation, and Computer Generation,
271
6.7
Estimation,
272
6.7.1
Classical Hypergeometric Distribution,
273
6.7.2
Negative (Inverse) Hypergeometric Distribution:
Beta-Binomial Distribution,
274
6.7.3
Beta-Pascal Distribution,
276
6.8
Characterizations,
277
6.9
Applications,
279
6.9.1
Classical Hypergeometric Distribution,
279
6.9.2
Negative (Inverse) Hypergeometric Distribution:
Beta-Binomial Distribution,
281
6.9.3
Beta-Negative Binomial Distribution: Beta-Pascal
Distribution, Generalized Waring Distribution,
283
6.10
Special Cases,
283
6.10.1
Discrete
Rectangular
Distribution, 283
6.10.2 Distribution
of Leads in Coin Tossing,
286
6.10.3
Yule Distribution,
287
6.10.4
Waring Distribution,
289
6.10.5
Narayana Distribution,
291
6.11
Related Distributions,
293
6.11.1
Extended Hypergeometric Distributions,
293
6.11.2
Generalized Hypergeometric Probability
Distributions,
296
6.11.3
Generalized Hypergeometric Factorial Moment
Distributions,
298
6.11.4
Other Related Distributions,
299
7
Logarithmic and Lagrangian Distributions
302
7.1
Logarithmic Distribution,
302
7.1.1
Definition,
302
7.1.2
Historical Remarks and Genesis,
303
7.1.3
Moments,
305
7.1.4
Properties,
307
7.1.5
Approximations and Bounds,
309
7.1.6
Computation, Tables, and Computer
Generation,
310
7.1.7
Estimation,
311
7.1.8
Characterizations,
315
7.1.9
Applications,
316
7.1.10
Truncated and Modified Logarithmic
Distributions,
317
7.1.11
Generalizations of the Logarithmic Distribution,
319
7.1.12
Other Related Distributions,
321
7.2
Lagrangian Distributions,
325
7.2.1
Otter's Multiplicative Process,
326
7.2.2
Borei
Distribution,
328
7.2.3
Consul Distribution,
329
7.2.4
Geeta Distribution,
330
7.2.5
General Lagrangian Distributions of the First
Kind,
331
7.2.6
Lagrangian
Poisson
Distribution,
336
7.2.7
Lagrangian Negative Binomial Distribution,
340
7.2.8
Lagrangian Logarithmic Distribution,
341
7.2.9
Lagrangian Distributions of the Second Kind,
342
і
Mixture Distributions
343
8.1
Basic Ideas,
343
8.1.1
Introduction,
343
8.1.2
Finite Mixtures,
344
8.1.3
Varying Parameters,
345
8.1.4
Bayesian Interpretation,
347
8.2
Finite Mixtures of Discrete Distributions,
347
8.2.1
Parameters of Finite Mixtures,
347
8.2.2
Parameter Estimation,
349
8.2.3
Zero-Modified and Hurdle Distributions,
351
8.2.4
Examples of Zero-Modified Distributions,
353
8.2.5
Finite
Poisson
Mixtures,
357
8.2.6
Finite Binomial Mixtures,
358
8.2.7
Other Finite Mixtures of Discrete Distributions,
359
8.3
Continuous and Countable Mixtures of Discrete
Distributions,
360
8.3.1
Properties of General Mixed Distributions,
360
8.3.2
Properties of Mixed
Poisson
Distributions,
362
8.3.3
Examples of
Poisson
Mixtures,
365
8.3.4
Mixtures of Binomial Distributions,
373
8.3.5
Examples of Binomial Mixtures,
374
8.3.6
Other Continuous and Countable Mixtures of
Discrete Distributions,
376
8.4
Gamma and Beta Mixing Distributions,
378
9
Stopped-Sum Distributions
381
9.1
Generalized and Generalizing Distributions,
381
9.2
Damage Processes,
386
9.3
Poisson-
Stopped Sum (Multiple
Poisson)
Distributions,
388
9.4
Hermite Distribution,
394
9.5
Poisson-Binomial Distribution,
400
9.6
Neyman Type A Distribution,
403
9.6.1
Definition,
403
9.6.2
Moment Properties,
405
9.6.3
Tables and Approximations,
406
9.6.4
Estimation,
407
9.6.5
Applications,
409
9.7
Pólya-Aeppli
Distribution,
410
9.8
Generalized
Pólya-Aeppli
(Poisson-Négative
Binomial)
Distribution,
414
9.9
Generalizations of Neyman Type A Distribution,
416
9.10
Thomas Distribution,
421
9.11
Borel-Tanner Distribution: Lagrangian
Poisson
Distribution,
423
9.12
Other Poisson-Stopped Sum (multiple
Poisson)
Distributions,
425
9.13
Other Families of Stopped-Sum Distributions,
426
10
Matching, Occupancy, Runs, and
q
-Series Distributions
430
10.1
Introduction,
430
10.2
Probabilities of Combined Events,
431
10.3
Matching Distributions,
434
10.4
Occupancy Distributions,
439
10.4.1
Classical Occupancy and Coupon Collecting,
439
10.4.2
Maxwell-
В
oltzmann, Bose-Einstein, and
Fermi-Dirac Statistics,
444
10.4.3
Specified Occupancy and Grassia-Binomial
Distributions,
446
10.5
Record Value Distributions,
448
10.6
Runs Distributions,
450
10.6.1
Runs of Like Elements,
450
10.6.2
Runs Up and Down,
453
10.7
Distributions of Order k,
454
10.7.1
Early Work on Success Runs Distributions,
454
10.7.2
Geometric Distribution of Order k,
456
10.7.3
Negative Binomial Distributions of Order k,
458
10.7.4
Poisson
and Logarithmic Distributions of
Order k,
459
10.7.5
Binomial Distributions of Order k,
461
10.7.6
Further Distributions of Order k,
463
10.8
^-Series Distributions,
464
10.8.1
Terminating Distributions,
465
10.8.2
g-Series Distributions with Infinite Support,
470
10.8.3
Bilateral ^-Series Distributions,
474
10.8.4
^-Series Related Distributions,
476
11
Parametric
Regression Models
and Miscellanea
478
11.1
Parametric Regression Models,
478
11.1.1
Introduction,
478
11.1.2
Tweedie-Poisson Family,
480
11.1.3
Negative Binomial Regression Models,
482
11.1.4
Poisson
Lognormal
Model,
483
11.1.5
Poisson-Inverse
Gaussian
(Sichel)
Model,
484
11.1.6
Poisson
Polynomial Distribution,
487
11.1.7
Weighted
Poisson
Distributions,
488
11.1.8
Double-Poisson
and Double-Binomial
Distributions,
489
11.1.9
Simplex-Binomial Mixture Model,
490
11.2
Miscellaneous Discrete Distributions,
491
11.2.1
Dandekar's Modified Binomial and
Poisson
Models,
491
11.2.2
Digamma
and Trigamma Distributions,
492
11.2.3
Discrete
Adès
Distribution,
494
11.2.4
Discrete Bessel Distribution,
495
11.2.5
Discrete
Mittag
-Leffler Distribution,
496
11.2.6
Discrete Student's
t
Distribution,
498
11.2.7
Feller-Arley and
Gegenbauer
Distributions,
499
11.2.8
Gram-Charlier Type
В
Distributions,
501
11.2.9
"Interrupted" Distributions,
502
11.2.10
Lost-Games Distributions,
503
11.2.11
Luria-Delbriick Distribution,
505
11.2.12
Naor'
s
Distribution,
507
11.2.13
Partial-Sums Distributions,
508
11.2.14
Queueing Theory Distributions,
512
11.2.15
Reliability and Survival Distributions,
514
11.2.16
Skellam-Haldane Gene Frequency Distribution,
519
11.2.17
Steyn's Two-Parameter Power Series
Distributions,
521
11.2.18
Univariate Multinomial-Type Distributions,
522
11.2.19
Urn Models with Stochastic Replacements,
524
11.2.20
Zipf-Related Distributions,
526
11.2.21
Haighť s
Zeta
Distributions,
533
Bibliography
Abbreviations
Index
535
631
633
The Third Edition of the critically acclaimed Univariate Discrete Distributions provides
a self-contained, systematic treatment of the theory, derivation, and application of
probability distributions for count data. Generalized zeta-function and q-series
distributions have been added and are covered in detail. New families of distributions,
including Lagrangian-type distributions, are integrated into this thoroughly revised
and updated text. Additional applications of univariate discrete distributions are
explored to demonstrate the flexibility of this powerful method.
A thorough survey of recent statistical literature draws attention to many
new distributions and results for the classical distributions. Approximately
450
new
references along with several new sections are introduced to reflect the current
literature and knowledge of discrete distributions.
Beginning with mathematical, probability, and statistical fundamentals, the authors
provide clear coverage of the key topics in the field, including:
•
Families of discrete distributions
•
Binomial distribution
•
Poisson
distribution
•
Negative binomial distribution
•
Hypergeometric distributions
•
Logarithmic and Lagranglan distributions
•
Mixture distributions
•
Stopped-sum distributions
•
Matching, occupancy, runs, and q-series distributions
•
Parametric regression models and miscellanea
Emphasis continues to be placed on the increasing relevance of Bayesian inference to
discrete distribution, especially with regard to the binomial and
Poisson
distributions.
New derivations of discrete distributions via stochastic processes and random walks
are introduced without unnecessarily complex discussions of stochastic processes.
Throughout the Third Edition, extensive information has been added to reflect the new
role of computer-based applications.
With Its thorough coverage and balanced presentation of theory and application, this
is an excellent and essential reference for statisticians and mathematicians. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Johnson, Norman Lloyd 1917-2004 Kemp, Adrienne W. Kotz, Samuel 1930-2010 |
| author_GND | (DE-588)128650419 (DE-588)119529653 |
| author_facet | Johnson, Norman Lloyd 1917-2004 Kemp, Adrienne W. Kotz, Samuel 1930-2010 |
| author_role | aut aut aut |
| author_sort | Johnson, Norman Lloyd 1917-2004 |
| author_variant | n l j nl nlj a w k aw awk s k sk |
| building | Verbundindex |
| bvnumber | BV023074449 |
| callnumber-first | Q - Science |
| callnumber-label | QA273 |
| callnumber-raw | QA273.6 |
| callnumber-search | QA273.6 |
| callnumber-sort | QA 3273.6 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 233 SK 835 |
| classification_tum | MAT 603f |
| ctrlnum | (OCoLC)57484554 (DE-599)BVBBV023074449 |
| dewey-full | 519.2/4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/4 |
| dewey-search | 519.2/4 |
| dewey-sort | 3519.2 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV023074449 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T19:34:29Z |
| indexdate | 2024-07-09T21:10:24Z |
| institution | BVB |
| isbn | 0471272469 9780471272465 |
| language | English |
| lccn | 2005019970 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016277563 |
| oclc_num | 57484554 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-83 DE-739 DE-91G DE-BY-TUM DE-578 DE-11 DE-M382 |
| owner_facet | DE-355 DE-BY-UBR DE-83 DE-739 DE-91G DE-BY-TUM DE-578 DE-11 DE-M382 |
| physical | XIX, 646 S. 24 cm |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Wiley-Interscience |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Johnson, Norman Lloyd 1917-2004 Verfasser (DE-588)128650419 aut Univariate discrete distributions Norman L. Johnson ; Adrienne W. Kemp ; Samuel Kotz 3. ed. Hoboken, NJ [u.a.] Wiley-Interscience 2005 XIX, 646 S. 24 cm txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics 1st. ed. u.d.T.: Discrete distributions Includes bibliographical references (p. 535-630) and index Distribution (Théorie des probabilités) Univariate methoden gtt Verdelingen (statistiek) gtt Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd rswk-swf Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 s DE-604 Kemp, Adrienne W. Verfasser aut Kotz, Samuel 1930-2010 Verfasser (DE-588)119529653 aut http://www.loc.gov/catdir/toc/ecip0515/2005019970.html Table of contents only http://www.loc.gov/catdir/enhancements/fy0622/2005019970-b.html Contributor biographical information http://www.loc.gov/catdir/enhancements/fy0622/2005019970-d.html Publisher description Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016277563&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016277563&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Johnson, Norman Lloyd 1917-2004 Kemp, Adrienne W. Kotz, Samuel 1930-2010 Univariate discrete distributions Distribution (Théorie des probabilités) Univariate methoden gtt 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_exact_search_txtP | Univariate discrete distributions |
| title_full | Univariate discrete distributions Norman L. Johnson ; Adrienne W. Kemp ; Samuel Kotz |
| title_fullStr | Univariate discrete distributions Norman L. Johnson ; Adrienne W. Kemp ; Samuel Kotz |
| title_full_unstemmed | Univariate discrete distributions Norman L. Johnson ; Adrienne W. Kemp ; Samuel Kotz |
| title_short | Univariate discrete distributions |
| title_sort | univariate discrete distributions |
| topic | Distribution (Théorie des probabilités) Univariate methoden gtt Verdelingen (statistiek) gtt Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung (DE-588)4150184-6 gnd |
| topic_facet | Distribution (Théorie des probabilités) Univariate methoden Verdelingen (statistiek) Distribution (Probability theory) Diskrete Wahrscheinlichkeitsverteilung |
| url | http://www.loc.gov/catdir/toc/ecip0515/2005019970.html http://www.loc.gov/catdir/enhancements/fy0622/2005019970-b.html http://www.loc.gov/catdir/enhancements/fy0622/2005019970-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016277563&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016277563&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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