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 language | English |
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Pages (from-to) | 1977-2001 |
Number of pages | 25 |
Journal | Communications in Statistics - Theory and Methods |
Volume | 31 |
Issue number | 11 |
DOIs | |
Publication status | Published - 2002 |
Keywords
- Accident model
- Data grouping
- Pearson's X
- Regression
- Scaled deviance