Numerical Comparisons for the Null Distribution of the Bagai Statistic
- Authors
- 하형태
- Issue Date
- Mar-2012
- Publisher
- 한국통계학회
- Keywords
- The Bagai statistic; null distribution; numerical comparisons; Gaussian-polynomial approximation; saddlepoint approximation; cumulant generating function; moments.
- Citation
- Communications for Statistical Applications and Methods, v.19, no.2, pp.267 - 276
- Journal Title
- Communications for Statistical Applications and Methods
- Volume
- 19
- Number
- 2
- Start Page
- 267
- End Page
- 276
- URI
- https://scholarworks.bwise.kr/gachon/handle/2020.sw.gachon/80792
- ISSN
- 2287-7843
- 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 Gaussian-polynomial 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.
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