Numerical Comparisons for the Null Distribution of the Bagai Statistic

- Journal title : Communications for Statistical Applications and Methods
- Volume 19, Issue 2, 2012, pp.267-276
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2012.19.2.267

Title & Authors

Numerical Comparisons for the Null Distribution of the Bagai Statistic

Ha, Hyung-Tae;

Ha, Hyung-Tae;

Abstract

Bagai et al. (1989) proposed a distribution-free test for stochastic ordering in the competing risk model, and recently Murakami (2009) utilized a standard saddlepoint approximation to provide tail probabilities for the Bagai statistic under finite sample sizes. In the present paper, we consider the Gaussian-polynomial approximation proposed in Ha and Provost (2007) and compare it to the saddlepoint approximation in terms of approximating the percentiles of the Bagai statistic. We make numerical comparisons of these approximations for moderate sample sizes as was done in Murakami (2009). From the numerical results, it was observed that the Gaussianpolynomial approximation provides comparable or greater accuracy in the tail probabilities than the saddlepoint approximation. Unlike saddlepoint approximation, the Gaussian-polynomial approximation provides a simple explicit representation of the approximated density function. We also discuss the details of computations.

Keywords

The Bagai statistic;null distribution;numerical comparisons;Gaussian-polynomial approximation;saddlepoint approximation;cumulant generating function;moments;

Language

English

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