Abstract
Some of the well known discrete distributions arise in a natural way through lattice path combinatorics (Mohanty, 1979). In this paper, we consider some discrete distributions from another point of view — as special cases of a generalized four-parameter Charlier distribution. Some properties of the distribution including recurrence relations for the mass function as well as for the moments and cumulants of the distribution are obtained. The distribution includes, as particular cases, negative binomial, Gegenbauer, and generalized Charlier distributions. Methods for fitting a three-parameter generalized Charlier distribution are indicated. The results are applied to data to which distributions were fitted earlier by Beall and Rescia ( Biometrics, 1953) and Katti and Gurland ( Biometrics, 1961). The distribution considered here appears to give better fit.
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