期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2005
卷号：67
期号：03
出版社：Indian Statistical Institute
摘要：A general method is proposed for testing the fit to any member of the invariant under convolutions family of count models, parameterized by mean and variance. The test statistics, which are of the weighted L2-type, exploit the specific structure of the corresponding probability generating function. Their asymptotic null distribution is obtained, and the consistency of the tests is studied. As an example, the generalized Hermite distribution, a specific member of this family, is analysed. In this case, two methods of estimation of the parameters are considered, for which limit statistics are obtained as the decay of the weight function tends to infinity. The performance of a parametric bootstrap version of the method is investigated via Monte Carlo.
关键词：Empirical probability generating function, bootstrap test, Poisson distribution.
