Inference for Sichel's Compound Poisson Distribution
作者:
A.C. Atkinson,
Lam Yeh,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1982)
卷期:
Volume 77,
issue 377
页码: 153-158
ISSN:0162-1459
年代: 1982
DOI:10.1080/01621459.1982.10477779
出版商: Taylor & Francis Group
关键词: Approximate likelihood;Compound Poisson distribution;Modified Bessel functions of the second and third kinds;Score statistic
数据来源: Taylor
摘要:
In a long-tailed compound Poisson distribution introduced by Sichel, the probabilities can only readily be calculated if one of the parameters λ has half-integer values, that is, λ =m+ 1/2,minteger. The maximum likelihood estimation of this parameter is compared with an approximate method derived from a grid of half-integer values. It is found that the approximate method, which avoids excessive special computation, yields inferences indistinguishable from those based on maximum likelihood and on the score statistic for testing values of λ. Thus a major numerical impediment to use of Sichel's distribution is removed.
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