Some bivariate Schur-constant distributions and application to life insurance

Abstract

Schur-constant models play a particular role when modelling time in fields such as actuarial science, insurance, reliability and survival models. These models describe random lifetimes with a certain dependence. In this study, a relation between proportional hazard rate distributions and Schur-constant models is established. Bivariate Schur-constant models, whose marginals are proportional hazard rate distributed, are introduced. Then, the dependency analysis in life insurances is performed through Schur-constant and copula models. It is revealed that there are differences in pricing when individuals' future lifetimes are dependent.