The Sibling Distribution for Multivariate Life Time Data

Abstract

A flexible class of multivariate distributions for continuous lifetimes is proposed. The distribution is defined in terms of the age-at-death of m siblings. The expression for the joint density is derived using classical results from mathematical demography. The parameters of the distribution are the age-specific birth and death rates, in addition to a vector of relative death times for the m siblings. For the case of constant birth and death rates we are able to derive an explicit expression for the bivariate sibling density, which is proven to be MTP2, and hence has positive dependence. Further, we show that a special case of the sibling distribution belongs to the Block-Basu class of multivariate distribution. In the general case, with age-dependent birth and death rates, evaluation of the density involves numerical integration, but is still feasible.