Volume 11, February 2007Special Issue: "Stochastic analysis and mathematical finance" in honor of Nicole El Karoui's 60th birthday
|Page(s)||248 - 263|
|Published online||19 June 2007|
Polynomial expansions of density of power mixtures
CREST - ENSAI, Rue Blaise Pascal, BP 37203, 35172
Bruz Cedex, France; firstname.lastname@example.org
Revised: 21 June 2006
Revised: 1 December 2006
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
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