Introduction to parametric survival models and their estimation

• Main Author: Manning, Thomas Q.
• Format: text
• Language: English
• Published: Animo Repository 1996
• Subjects: Mathematical models; Parameter estimation; Estimation theory; Least squares
• Online Access: https://animorepository.dlsu.edu.ph/etd_bachelors/16345
• Institution: De La Salle University

This thesis discusses the different kinds of parametric survival models. These models are based on special statistical distributions. There are five models used in the discussion namely: the Uniform, Exponential, Gompertz, Makeham, and Weibull distributions. These models are discussed in different statistics' books. Mainly, the material for this paper is based on the book entitled, Survival Models and Their Estimation by Dick London, FSA. Estimation of parametric survival models involves the estimation of the different parameters within each model. Mainly, the researcher discusses the methods in which these parameters are estimated. The models being discussed in this thesis involves the use of only one random variable, time. The discussion is then limited to the univariate model. There are two types of data that are used in the methods of estimation. These are the exact times of death and the grouped times of death. Both of these are used in the discussion involving the complete data set. However, only the grouped times of death data set is used in the incomplete data set discussion. There are different methods of estimation being discussed in this thesis. The main approaches are the methods of maximum likelihood and the method of least squares. These approaches are used in both the complete data set and the incomplete data set. The other approaches used are the method of means, medians, and percentiles. The last topic of discussion in this thesis involves a method for obtaining a more appropriate estimate for the parameters.