INTERRELATIONSHIPS BETWEEN l_P‐ISOTROPIC DENSITIES AND l_P‐ISOTROPIC SURVIVAL FUNCTIONS, AND DE FINETTI REPRESENTATIONS OF SCHUR‐CONCAVE SURVIVAL FUNCTIONS

Interrelationships between l_P‐isotropic densities and l_P‐isotropic survival functions are studied. We obtain representations for densities whose survival functions are l_P‐isotropic and for survival functions whose densities are l_P‐isotiopic. The former are mixtures of products of Weibull densities and the latter are mixtures of products of Gamma survival functions. Based on a theorem proved by Cooke, we show that de Finetti representations for Schur‐concave survival functions that have the same level sets as a product measure can be represented as mixtures of products of increasing failure rate survival functions.