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Henze, Norbert; Klar, Bernhard

Bootstrap based goodness of fit tests for the generalized Poisson model. (English) Zbl 0937.62586

Commun. Stat., Theory Methods 24, No. 7, 1875-1896 (1995).
Summary: Due to its versatile nature, the Generalized Poisson distribution (\(GPD\)) of P. C. Consul and G. C. Jain [Technometrics 15, 791-799 (Zbl 0271.60020; 1973)] has been an object of sustained interest. However, apart from the classical \(\chi^2\)-test with its inherent problems, there is a paucity of genuine goodness of fit tests for checking the \(GPD\) model on the basis of given data. In this paper we study empirical distribution function based tests for the \(GPD\) model. A key tool is a weak convergence result for an estimated (discrete) empirical process, regarded as a random element in some suitable sequence space. A parametric bootstrap version of the procedure is shown to maintain a desired level of significance very closely even for small sample sizes. The test is applied to data sets of frequencies of the duration of atmospheric circulation patterns.

Cited in 5 Documents

MSC:

62G09 Nonparametric statistical resampling methods
62G10 Nonparametric hypothesis testing

Keywords:

generalized Poisson distribution; goodness of fit test; empirical distribution function; weak convergence; parametric bootstrap; atmospheric circulation patterns; 272

Citations:

Zbl 0271.60020
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Full Text: DOI

References:

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