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http://dx.doi.org/10.7465/jkdi.2013.24.6.1211

Saddlepoint approximation for distribution function of sample mean of skew-normal distribution  

Na, Jong-Hwa (Department of Information and Statistics, Chungbuk National University)
Yu, Hye-Kyung (Korea National Institute of Health)
Publication Information
Journal of the Korean Data and Information Science Society / v.24, no.6, 2013 , pp. 1211-1219 More about this Journal
Abstract
Recently, the usage of skew-normal distribution, instead of classical normal distribution, is rising up in many statistical theories and applications. In this paper, we deal with saddlepoint approximation for the distribution function of sample mean of skew-normal distribution. Comparing to normal approximation, saddlepoint approximation provides very accurate results in small sample sizes as well as for large or moderate sample sizes. Saddlepoint approximations related to the skew-normal distribution, suggested in this paper, can be used as a approximate approach to the classical method of Gupta and Chen (2001) and Chen et al. (2004) which need very complicate calculations. Through simulation study, we verified the accuracy of the suggested approximation and applied the approximation to Robert's (1966) twin data.
Keywords
Cumulant generating function; saddlepoint approximation; sample mean; skew-normal distribution;
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Times Cited By KSCI : 3  (Citation Analysis)
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