The aim of the research is the statistical modelling of parametric survival distributions of grouped survival data of long- and shortterm policies in the insurance industry, by means of a method of maximum likelihood estimation subject to constraints. This methodology leads to explicit expressions for the estimates of the parameters, as well as for approximated variances and covariances of the estimates, which gives exact maximum likelihood estimates of the parameters. This makes direct extension to more complex designs feasible. The statistical modelling offers parametric models for survival distributions, in contrast with non-parametric models that are used commonly in the actuarial profession. When the parametric models provide a good fit to data, they tend to give more precise estimates of the quantities of interest such as odds ratios, hazard ratios or median lifetimes. These estimates form the statistical foundation for scientific decisionmaking with respect to actuarial design, maintenance and marketing of insurance policies. Although the methodology in this thesis is developed specifically for the insurance industry, it may be applied in the normal context of research and scientific decision making, that includes for example survival distributions for the medical, biological, engineering, econometric and sociological sciences.
Dissertation (PhD (Mathematical Statistics))--University of Pretoria, 2006.