A weak version of bivariate lack of memory property

Abstract

We suggest a modification of the classical Marshall-Olkin's bivariate exponential distribution considering a possibility of a singularity contribution along arbitrary line through the origin. It serves as a base of a weak version of the bivariate lack of memory property, which might be both "aging" and "non-aging' depending on the additional inclination (skew) parameter. The corresponding copula is obtained and we establish its disagreement with Lancaster's phenomena. Characterizations and properties of the novel bivariate memory-less notion are obtained and its applications are discussed. We characterize related weak multivariate version. The weak bivariate lack of memory property implies restrictions on associated marginal distributions. Starting from pre-specified marginals we propose a procedure to build bivariate distributions possessing a weak bivariate lack of memory property and illustrate it by examples. We complement the methodology with closure properties of the new class. We finish with a discussion and suggest several problems for a future research.

Joint Life Insurance Pricing Using Extended Marshall–olkin Models

“…In order to describe the dependencies in the joint life survival status, the model (1.1) has been applied by many authors (see Chapter 9 of Bowers et al (1997), Denuit et al (2006) and references therein). The stochastic representation (1.1) has been recently improved by Kolev and Pinto (2018) considering the relation…”