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Polynomial expansions of density of power mixtures

Published online by Cambridge University Press:  19 June 2007

Denys Pommeret
Denys Pommeret*
Affiliation:
CREST - ENSAI, Rue Blaise Pascal, BP 37203, 35172 Bruz Cedex, France; pommeret@ensai.fr
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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.

Keywords

Approximationconvolutionerror boundgoodness-of-fit testmixed distributionorthogonal polynomialsscale mixture.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 11: Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthdaySpecial Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday , June 2007 , pp. 248 - 263
Copyright
© EDP Sciences, SMAI, 2007

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