Open Access
December 2004 Saddlepoint approximation for moment generating functions of truncated random variables
Ronald W. Butler, Andrew T. A. Wood
Ann. Statist. 32(6): 2712-2730 (December 2004). DOI: 10.1214/009053604000000689


We consider the problem of approximating the moment generating function (MGF) of a truncated random variable in terms of the MGF of the underlying (i.e., untruncated) random variable. The purpose of approximating the MGF is to enable the application of saddlepoint approximations to certain distributions determined by truncated random variables. Two important statistical applications are the following: the approximation of certain multivariate cumulative distribution functions; and the approximation of passage time distributions in ion channel models which incorporate time interval omission. We derive two types of representation for the MGF of a truncated random variable. One of these representations is obtained by exponential tilting. The second type of representation, which has two versions, is referred to as an exponential convolution representation. Each representation motivates a different approximation. It turns out that each of the three approximations is extremely accurate in those cases “to which it is suited.” Moreover, there is a simple rule of thumb for deciding which approximation to use in a given case, and if this rule is followed, then our numerical and theoretical results indicate that the resulting approximation will be extremely accurate.


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Ronald W. Butler. Andrew T. A. Wood. "Saddlepoint approximation for moment generating functions of truncated random variables." Ann. Statist. 32 (6) 2712 - 2730, December 2004.


Published: December 2004
First available in Project Euclid: 7 February 2005

zbMATH: 1068.62015
MathSciNet: MR2154000
Digital Object Identifier: 10.1214/009053604000000689

Primary: 62E15
Secondary: 62E17

Keywords: Exponentially convoluted , saddlepoint approximation , tilted distribution , truncated distribution

Rights: Copyright © 2004 Institute of Mathematical Statistics

Vol.32 • No. 6 • December 2004
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