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On the Student's t-distribution and the t-statistic

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  • Yang, Zhenhai
  • Fang, Kai-Tai
  • Kotz, Samuel

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, Sankhya, 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.

Suggested Citation

  • Yang, Zhenhai & Fang, Kai-Tai & Kotz, Samuel, 2007. "On the Student's t-distribution and the t-statistic," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1293-1304, July.
  • Handle: RePEc:eee:jmvana:v:98:y:2007:i:6:p:1293-1304
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    1. Yang, Zhenhai & Kotz, Samuel, 2003. "Center-similar distributions with applications in multivariate analysis," Statistics & Probability Letters, Elsevier, vol. 64(4), pages 335-345, October.
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