Assessing goodness of fit for Poisson and negative binomial models with low mean

G. R. Wood*

*Corresponding author for this work

    Research output: Contribution to journalArticle

    2 Citations (Scopus)

    Abstract

    Testing goodness of fit for a Poisson distribution is routine when the mean is sufficiently large; the scaled deviance G2 or Pearson's X2 statistic follow approximate chi-square distributions and perform the task well. When the mean is low, typically less than one, the approximations to chi-square distributions are poor. In this paper we explore the underlying reasons for this behaviour and present a practical resolution of the problem, in both single distribution and regression contexts. An extension to negative binomial models is also given. This research is motivated by a real example drawn from road accident modelling.

    Original languageEnglish
    Pages (from-to)1977-2001
    Number of pages25
    JournalCommunications in Statistics - Theory and Methods
    Volume31
    Issue number11
    DOIs
    Publication statusPublished - 2002

    Keywords

    • Accident model
    • Data grouping
    • Pearson's X
    • Regression
    • Scaled deviance

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