Parameter Orthogonality for a Family of Discrete Distributions

Abstract

Abstract The standard contagious distributions (see Douglas 1980) have been used in such varied fields as biology and automobile insurance, often to model various physical phenomena as well as provide a good fit to count data when other models are inadequate. Unfortunately, the parameterizations often used when working with these distributions normally lead to extremely high correlations of the maximum likelihood estimators (MLE's). This tends to lead to mathematical complexities, and causes difficulty or even errors in their interpretation. Furthermore, numerical difficulties may arise when using numerical procedures to locate the estimates. Some of these difficulties were discussed by Douglas (1980, pp. 171, 204-205), who suggested that a reparameterization to reduce or even eliminate such correlation is desirable. If the MLE's are asymptotically uncorrelated, the parameterization is orthogonal. Philpot (1964) derived an orthogonal parameterization for the Neyman Type A distribution; Stein, Zucchini, an...