Frontiers of Mathematics in China >

2011 , Vol. 6 >Issue 6: 1265 - 1284

DOI: https://doi.org/10.1007/s11464-011-0128-7

RESEARCH ARTICLE

Saddlepoint approximation for moments of random variables

  • Kai ZHAO 1 ,
  • Xue CHENG , 1,2 ,
  • Jingping YANG 1,2
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  • 1. Department of Financial Mathematics, Center for Statistical Science, Peking University, Beijing 100871, China
  • 2. Key Lab of Mathematics and Applied Mathematics (Peking University), Ministry of Education, Beijing 100871, China

Received date: 15 Oct 2010

Accepted date: 10 Mar 2011

Published date: 01 Dec 2011

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

In this paper, we introduce a saddlepoint approximation method for higher-order moments like E(S-a)+m, a>0, where the random variable S in these expectations could be a single random variable as well as the average or sum of some i.i.d random variables, and a>0 is a constant. Numerical results are given to show the accuracy of this approximation method.

Key words： Saddlepoint approximation; higher moments; sum of i.i.d. random variables

Cite this article

Kai ZHAO , Xue CHENG , Jingping YANG . Saddlepoint approximation for moments of random variables[J]. Frontiers of Mathematics in China, 2011 , 6(6) : 1265 -1284 . DOI: 10.1007/s11464-011-0128-7

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