The spatial modeling of a mixture distribution

The mixture of discrete and continuous distributions was first considered by Aitchison (1955) and is called the Delta-Distribution. Pennington (1983) obtained the uniform minimum variance unbiased estimators for parameters of the Delta-Distribution under conditions that the distributions are identically independent distributions (i.i.d). Stefansson (1996) introduced spatial patterns into the Delta-Distribution which were assumed to be independent, but not necessarily identically distributed. For the exponential family with spatial correlation, Besag (1974) introduced the method of quasi-likelihood and Liang and Zeger (1986) provided the method of quasi-likelihood. However, both procedures required certain conditions to be satisfied and there are no general asymptotic results for these estimators.;In this dissertation, the pseudo-likelihood and the quasi-likelihood procedures are used to estimate the parameters of the Delta-Distribution. The general conditions needed to use the pseudo-likelihood procedure are found. The quasi-likelihood estimators are extended to a new estimator which has excellent asymptotic properties. A simulation study is used to evaluate the fixed sample size properties of these estimators. The model is also used to analyze a data set from marine science.