On a Contagious Distribution Suggested for Accident Data

Abstract

Cresswell & Froggatt [1963] devised a model leading to a three-parameter distribution, which they called the 'Short' distribution, to describe accident data. It is the convolution of a Poisson distribution and a Neyman Type A distribution. We consider first its general properties. Then we derive a recurrence relationship for the probabilities, and also the maximum-likelihood equations, from the probability generating function by a very simple differentiation method. An Algol program has been written to solve these equations and a numerical example is given. The efficiency of the method of moments for estimating the parameters is also examined. Results suggest that, in general, because of extremely high correlations between them, the estimates of the parameters (by either method) will be subject to very large sampling errors. This implies severe limitations on the use of the distribution.