Fourier Series Approximation for the Generalized Baumgartner Statistic

- Journal title : Communications for Statistical Applications and Methods
- Volume 19, Issue 3, 2012, pp.451-457
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2012.19.3.451

Title & Authors

Fourier Series Approximation for the Generalized Baumgartner Statistic

Ha, Hyung-Tae;

Ha, Hyung-Tae;

Abstract

Baumgartner et al. (1998) proposed a novel statistical test for the null hypothesis that two independently drawn samples of data originate from the same population, and Murakami (2006) generalized the test statistic for more than two samples. Whereas the expressions of the exact density and distribution functions of the generalized Baumgartner statistic are not yet found, the characteristic function of its limiting distribution has been obtained. Due to the development of computational power, the Fourier series approximation can be readily utilized to accurately and efficiently approximate its density function based on its Laplace transform. Numerical examples show that the Fourier series method provides an accurate approximation for statistical quantities of the generalized Baumgartner statistic.

Keywords

Fourier series approximation;generalized Baumgartner statistic;Laplace transform;limiting distributions;saddlepoint approximation;

Language

English

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