COMPETING RISK MODELS IN PRESENCE OF PROGRESSIVELY TYPE-II CENSORED DATA FOR DAGUM DISTRIBUTION

Abstract

In the survival time analysis, there could be more than one cause of failure for an individual or an item. Usually, researchers are interested in survival times under a certain cause of failure, considering the rest of the causes as "other". Moreover, censoring is unavoidable in survival analysis, due to the time and money limitations where researchers are unable to get comprehensive information for the entire units in the experiment. "Progressive Type-II censoring" is considered in this thesis of the problem of competing risks under the Dagum or "Burr Type-III" distribution. "Maximum likelihood" estimation is applied to estimate the unknown shape parameters under the general case as well as the special case of a common shape parameter. Moreover, the observed "Fisher information matrix" is found to get the approximate CI for the unknown parameters. The bootstrap CI is also studied using the resampling method. Furthermore, adequacy of the proposed methods are assessed using "Monte Carlo simulation" followed by an analysis of a real dataset.