Estimating Survival Functions in the Case of Three or More Stochastically Ordered Populations

Abstract

The time until the occurrence of an event of interest is a quantity that is often sought after by clinicians, engineers, and numerous other scientists for understanding lifetimes. Through scientific knowledge, it can be assumed that many distributions are stochastically ordered. Including a stochastic ordering constraint on estimators can vastly improve the bias and mean squared error properties of an estimator. Rojo (2004) developed a pair of estimators for the case of estimating two stochastically ordered survival functions. The goal of this research is to develop a generalization of Rojo’s estimators to accommodate for the case of estimating more than two survival functions. The quality of the estimators developed in this study is assessed through simulations, testing the estimators against a variety of scenarios. The estimator proposed in this research is shown to have better mean squared error properties than estimators proposed by Barmi and Mukerjee (2005) for cases with equal censoring rates. However, for cases with unequal censoring between distributions, Barmi and Mukerjee’s estimator performs better than the estimator proposed in this study.