Saddlepoint Approximations to the CDF of Some Statistics with Nonnormal Limit Distributions
作者:
AndrewT. A. Wood,
JamesG. Booth,
RonaldW. Butler,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1993)
卷期:
Volume 88,
issue 422
页码: 680-686
ISSN:0162-1459
年代: 1993
DOI:10.1080/01621459.1993.10476322
出版商: Taylor & Francis Group
关键词: Chi-squared;Cumulant generating function;Cumulative distribution function;First passage distribution;Random walk;Saddlepoint approximation
数据来源: Taylor
摘要:
In standard saddlepoint approximations to the cumulative distribution function of a random variable, the normal distribution has appeared to play a special role. In this article we consider what happens when the normal “base” distribution is replaced by an arbitrary base distribution. Generalized versions of several standard formulas, are presented. The choice of a chi-squared base or an inverse Gaussian base is then considered in detail. The generalized approximations are compared in two examples: a linear combination of chi-squared variables and the first passage time distribution for a random walk. The former example considers approximations using the chi-squared base that are slightly more accurate than their normal-based counterparts. In the latter example, approximations based on the inverse Gaussian are considerably more accurate than their normal-based counterparts.
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