BIVARIATE LIFE DISTRIBUTIONS FROM POLYAS-URN MODEL FOR CONTAGION

Shock models based on Poisson processes have been used to derive univa riate and multivariate exponential distributions. But in many applicat ions, Poisson processes are not realistic models of physical shock pro cesses because they have independent increments; expanded models that allow for possibly dependent increments are of interest. In this paper , univariate and bivariate Polya urn schemes are used to derive models of shock sources. The life distributions obtained from these models f orm a large parametric family that includes the exponential distributi on. Even in the univariate case these life distributions have not been widely used, though they form a large and flexible family. In the biv ariate case, the family includes the bivariate exponential distributio ns of Marshall and Olkin as a special case. AMS 1991 SUBJECT CLASSIFIC ATION: PRIMARY 60 E05 SECONDARY 62 E15