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Zbl 1181.60016
Pommeret, Denys
Polynomial expansions of density of power mixtures. (English)
[J] ESAIM, Probab. Stat. 11, 248-263 (2007). ISSN 1292-8100; ISSN 1262-3318/e

Summary: 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.

MSC 2000:: *60E05 General theory of probability distributions
62E17 Approximations to statistical distributions (nonasymptotic)

Keywords: approximation; convolution; error bound; goodness-of-fit test; mixed distribution; orthogonal polynomials; scale mixture

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