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Polynomial expansions of density of power mixtures
Denys Pommeret
Journal:

ESAIM: Probability and Statistics / Volume 11 / June 2007

Published online by Cambridge University Press:

19 June 2007, pp. 248-263

Print publication:

June 2007
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For any given random variable Y with infinitelydivisible distribution in a quadratic natural exponential family we obtain a polynomial expansion ofthe power mixture density of Y.We approach the problem generally, and then consider certain distributionsin greater detail.Various applications are indicated and the results are also appliedto obtain approximations and their error bounds.Estimation of density and goodness-of-fit test are derived.