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ON TESTING FOR THE NUMBER OF COMPONENTS

IN A MIXED POISSON MODEL

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DIMITRIS KARLIS AND EVDOKIA XEKALAKI

*Department of Statistics, Athens University of Economics and Business,*

76 Patission St., 10434, Athens, Greece
(Received May 22, 1996; revised November 10, 1997)

**Abstract.**
Poisson mixtures are
usually used to describe overdispersed data.
Finite Poisson mixtures are used in many
practical situations where often it is of
interest to determine the number of components
in the mixture. Identifying how many components
comprise a mixture remains a difficult problem.
The likelihood ratio test (LRT) is a general
statistical procedure to use. Unfortunately, a
number of specific problems arise and the
classical theory fails to hold. In this paper a
new procedure is proposed that is based on
testing whether a new component can be added to
a finite Poisson mixture which eventually leads
to the number of components in the mixture. It
is a sequential testing procedure based on the
well known LRT that utilises a resampling
technique to construct the distribution of the
test statistic. The application of the procedure
to real data reveals some interesting features
of the distribution of the test statistic.

*Key words and phrases*:
Poisson
mixture, *k*-finite mixture, number of
components, likelihood ratio test, resampling.

**Source**
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