Handbook of the Poisson distribution

Contents......Page 8
1.1 Definitions......Page 12
1.2 Relations between Exact and Cumulative Probabilities......Page 13
1.3 Relations Involving Moments......Page 16
1.4 Incomplete Moments and Related Formulas......Page 20
1.5 Other Parameters......Page 22
1.6 Generating Functions......Page 24
2.1 The Binomial Limit......Page 26
2.2 Limits of Other Distributions......Page 29
2.3 Some Special Probability Models......Page 30
2.4 The Poisson Process......Page 34
2.5 Distance between Events of a Poisson Process......Page 37
2.6 Poisson as Maximum Disorder Process......Page 39
3.1 Truncation of the Domain......Page 41
3.2 Linear Combinations of Poisson Variables......Page 44
3.3 Mixed Poisson Distributions......Page 46
3.4 The Polya Process......Page 50
3.5 Other Mixed Poisson Distributions......Page 51
3.6 Poisson Mixing......Page 54
3.7 Collective Risk Theory......Page 60
3.8 Stuttering Poisson Distribution......Page 63
3.9 Erlang Process......Page 67
3.10 Other Gap Distributions; Particle Counting......Page 68
3.11 Miscellaneous Generalizations......Page 70
3.12 Multivariate Poisson......Page 75
3.13 Consael Process......Page 77
4.1 The Normal Limit......Page 80
4.2 Sums of Poisson Variables; Sampling......Page 82
4.3 Differences of Poisson Variables......Page 85
4.4 Other Functions of Poisson Variables......Page 86
4.6 Properties of Poisson Processes......Page 88
4.7 Properties of Mixed Poisson Processes......Page 90
5.1 Poisson Distribution; Point Estimation......Page 93
5.2 Poisson Distribution; Interval Estimation......Page 96
5.3 Truncated Distributions......Page 98
5.4 Other Distributions......Page 102
6.1 Goodness of Fit Tests......Page 105
6.2 Fixed Sample Size Tests of A......Page 107
6.3 Sequential Tests of A......Page 108
6.4 Comparison of Two Samples......Page 109
6.5 Other Statistical Tests......Page 110
7.2 Agriculture and Ecology......Page 111
7.3 Biology......Page 112
7.4 Medicine......Page 113
7.6 Accidents......Page 114
7.7 Commerce......Page 115
7.9 Sociology and Demography......Page 116
7.11 Military......Page 117
7.13 Miscellaneous......Page 118
8.1 Probabilities and Parameters......Page 119
8.2 Estimation......Page 120
8.3 Hypothesis Testing......Page 122
9.1 Simeon Denis Poisson (1781-1840)......Page 124
9.3 Ladislaus von Bortkiewicz (1868-1931)......Page 125
9.4 From Bortkiewicz to Charlier (1898-1906)......Page 128
9.5 The Gini Controversy (1907-1910)......Page 129
9.6 Particle Counting; Differential-Difference Equations (1910-1913)......Page 130
9.7 Applications (1909-1915)......Page 131
9.8 The Whitaker Controversy (1914-1916)......Page 132
9.9 Generalizations (1917-1920)......Page 133
Reference List and Author Index......Page 135
Subject Index......Page 173