Document ESAIM: P&S, June 2007, Vol. 11, pp. 248-263
DOI: 10.1051/ps:2007017
Polynomial expansions of density of power mixtures
Denys PommeretCREST - ENSAI, Rue Blaise Pascal, BP 37203, 35172 Bruz Cedex, France; pommeret@ensai.fr
(Received March 15, 2006. Revised June 21, and December 1st, 2006. Published online 19 June 2007.)
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
Key words: Approximation, convolution, error bound, goodness-of-fit test, mixed distribution, orthogonal polynomials, scale mixture.
© EDP Sciences, SMAI 2007