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On the Student's t-distribution and the t-statistic
- Source :
-
Journal of Multivariate Analysis . Jul2007, Vol. 98 Issue 6, p1293-1304. 12p. - Publication Year :
- 2007
-
Abstract
- 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 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. [Copyright &y& Elsevier]
- Subjects :
- *DENSITY
*MATHEMATICS
*STATISTICS
*SCIENCE
Subjects
Details
- Language :
- English
- ISSN :
- 0047259X
- Volume :
- 98
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Journal of Multivariate Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 24697183
- Full Text :
- https://doi.org/10.1016/j.jmva.2006.11.003