Statistical inference for a bivariate exponential distribution based on grouped data

Abstract

Consider the bivariate exponential distribution due to Marshall and Olkin [2], whose survival function is$\bar F(x,y) = \exp [ - \lambda _1 x - \lambda _{2y} - \lambda _{12} \max (x,y)](x \geqslant 0,y \geqslant 0)$ with unknown parameters λ₁ > 0, λ₂ > 0 and λ₁₂ ≥ 0. Based on grouped data, a new estimator for λ₁, λ₂ and λ₁₂ is derived and its asymptotic properties are discussed. Besides, some test procedures of equal marginals and independence are given. A simulation result is given, too.