Bivariate Laplace transform of residual lives and their properties

Abstract

The Laplace transform order of residual life is viewed as a tool for the stochastic comparison of two life distributions. In this paper, we study new notions of stochastic comparisons based on the bivariate Laplace transform order of residual lives. We investigate relationships the new stochastic order has with other existing bivariate orders. The interpretation of the new orders and their applications in different contexts are also pointed out. We propose nonparametric estimators for the Laplace transform of bivariate residual lives and perform a simulation study. The usefulness of the estimators are also illustrated using a real data set.