Robust Bayesian Estimators For Survival Function Under Prior Data Conflict With Practical Application in the Health Side

Abstract

The analysis of survival functions is concerned with knowing how long humans will survive, This means studying and analyzing the time from the beginning of the disease to the end point of death. For example, the survival function of patients with heart attacks was studied and analyzed at Al Manathira General Hospital. The Weibull distribution was used to match the real data. The scale parameter & survival function have been estimated for Weibull distribution with have two parameters, this distribution was used in two cases, prior data unconflict & prior data conflict. A regular Bayes method & robust Bayes were used for estimation. We used inverse gamma distribution as a prior where it is a conjugate prior for Weibull distribution. Two simulation experiments have been used; the first experiment used was prior data unconflict where the regular Bayes method is the best for estimating the scale & survival function by using the integrated mean square error (IMSE) as a criterion for comparing. The second experiment is in the case of prior data conflict. The results showed that the robust Bayes method is the best for estimation of the scale parameter & survival function by using (IMSE).