Characterization properties of multivariate exponential distribution and their stability (Q914295)

The paper deals with Marshall and Olkin's n-dimensional generalization of the exponential distribution (M-O distribution). Let G(x) be the probability that an M-O distributed random vector exceeds the vector \(x\in {\mathbb{R}}^ n\) in all components simultaneously. Then \[ G(x+y)=G(x)G(y)\text{ for all } (x,y)\in M \] with a suitable \(M\subset {\mathbb{R}}^ n\times {\mathbb{R}}^ n\); this property also characterizes M-O distributions. The authors also investigate the stability of the characterization for the case \(n=2\), showing that a distribution with \(G(x+y)\) uniformly close to G(x)G(y) is close to an M-O distribution.