Some applications of the hypergeometric and Poisson distributions

1995 ◽  
pp. 30-60
Author(s):  
Henry C. Tuckwell
Keyword(s):  
Poisson Distributions

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

1990 ◽  
Vol 22 (2) ◽  
pp. 350-374 ◽  
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.

Poisson Distributions: Reply

1966 ◽  
Vol 17 (2) ◽  
pp. 192-193
Author(s):  
R. M. Adelson
Keyword(s):  
Poisson Distributions

The Binomial and Poisson Distributions

1968 ◽  
pp. 59-76
Author(s):  
H. Mulholland ◽  
C. R. Jones
Keyword(s):  
Poisson Distributions

scholarly journals Preliminary test-shrinkage estimators

1983 ◽  
Vol 2 (2) ◽  
pp. 88-91
Author(s):  
H. H. Lemmer
Keyword(s):  
Preliminary Test ◽  
Shrinkage Estimator ◽  
Shrinkage Estimators ◽  
Poisson Distributions

The advantages of using the very simple shrinkage estimator TL proposed by Lemmer rather than that proposed by Mehta and Srivivasan in the case of preliminary test estimators for parameters of the normal, binomial and Poisson distributions are examined.

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