Appendix C: Hypergeometric and Conditional Poisson Distributions

CONDITIONAL POISSON DISTRIBUTIONS

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964806060050 ◽

2005 ◽

Vol 20 (1) ◽

pp. 95-102

Author(s):

M. Zhou ◽

D. Yang ◽

Y. Wang ◽

S. Nadarajah

Keyword(s):

Special Functions ◽

Discrete Data ◽

Poisson Processes ◽

Discrete Distributions ◽

Continuous Data ◽

Poisson Distributions ◽

Conditional Poisson

Compared to the known univariate distributions for continuous data, there are relatively few available for discrete data. In this article, we derive a collection of 16 flexible discrete distributions by means of conditional Poisson processes. The calculations involve the use of several special functions and their properties.

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Identification of parameters of Poisson distributions by the extreme order statistics

Communications in Statistics - Simulation and Computation ◽

10.1080/03610918.2021.1928195 ◽

2021 ◽

pp. 1-7

Author(s):

Ping Sun

Keyword(s):

Order Statistics ◽

Identification Of Parameters ◽

Extreme Order Statistics ◽

Poisson Distributions

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Approximation of sums by compound Poisson distributions with respect to stop-loss distances

Advances in Applied Probability ◽

10.2307/1427540 ◽

1990 ◽

Vol 22 (2) ◽

pp. 350-374 ◽

Cited By ~ 31

Author(s):

S. T. Rachev ◽

L. Rüschendorf

Keyword(s):

Random Variables ◽

Independent Random Variables ◽

Compound Poisson ◽

Poisson Distributions ◽

Stop Loss ◽

Scale Transformations

The approximation of sums of independent random variables by compound Poisson distributions with respect to stop-loss distances is investigated. These distances are motivated by risk-theoretic considerations. In contrast to the usual construction of approximating compound Poisson distributions, the method suggested in this paper is to fit several moments. For two moments, this can be achieved by scale transformations. It is shown that the new approximations are more stable and improve the usual approximations by accompanying laws in examples where the probability 1 – pi that the ith summand is zero is not too large.

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