Polynomial expansions of density of power mixtures

Abstract

Abstract. For any given random variable Y with infinitely divisible distribution in a quadratic natural exponential family we obtain a polynomial expansion of the power mixture density of Y . We approach the problem generally, and then consider certain distributions in greater detail. Various applications are indicated and the results are also applied to obtain approximations and their error bounds. Estimation of density and goodness-of-fit test are derived.Mathematics Subject Classification. 60E05, 62E17.