On the Student's t-distribution and the t-statistic |
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Authors: | Zhenhai Yang Kai-Tai Fang Samuel Kotz |
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Affiliation: | a College of Applied Sciences, Beijing University of Technology, Beijing 10002, China b BNU-HKBU United International College, Zhuhai Campus of Beijing Normal University, Jinfenf Road, Zhuhai 519085, China c Department of Engineering Management, George Washington University, USA |
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Abstract: | In this paper we provide rather weak conditions on a distribution which would guarantee that the t-statistic of a random vector of order n follows the t-distribution with n-1 degrees of freedom. The results sharpen the earlier conclusions of Mauldon [Characterizing properties of statistical distributions, Quart. J. Math. 2(7) (1956) 155-160] and the more recent advances due to Bondesson [When is the t-statistic t-distributed, Sankhyā, Ser. A 45 (1983) 338-345]. The basic tool involved in the derivations is the vertical density representation originally suggested by Troutt [A theorem on the density of the density ordinate and an alternative interpretation of the Box-Muller method, Statistics 22(3) (1991) 463-466; Vertical density representation and a further remark on the Box-Muller method, Statistics 24 (1993) 81-83]. Several illustrative examples are presented. |
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Keywords: | 62E10 62E15 |
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