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EXPANSIONS FOR MOMENTS OF COMPOUND POISSON DISTRIBUTIONS

Published online by Cambridge University Press:  28 March 2013

S. Nadarajah ,
C.S. Withers  and
S.A.A. Bakar
S. Nadarajah
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK E-mail: saraless.nadarajah@manchester.ac.uk
C.S. Withers
Affiliation:
Applied Mathematics Group, Industrial Research Limited, Lower Hutt, New Zealand E-mail: c.withers@irl.cir.nz
S.A.A. Bakar
Affiliation:
Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia E-mail: saab@um.edu.my
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Abstract

Expansions for moments of $\overline{X}$, the mean of a random sample of size n, are given for both the univariate and multivariate cases. The coefficients of these expansions are simply Bell polynomials. An application is given for the compound Poisson variable SN, where $S_{n} = n \overline{X}$ and N is a Poisson random variable independent of X1, X2, …, yielding expansions that are computationally more efficient than the Panjer recursion formula and Grubbström and Tang's formula.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 27 , Issue 3 , July 2013 , pp. 319 - 331
Copyright
Copyright © Cambridge University Press 2013 

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