The Density of the t-Statistic for Non-normal Distributions
SOUTHERN METHODIST UNIV DALLAS TX DEPT OF STATISTICAL SCIENCE
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The joint density function of the sample mean and sample variance is recursively derived for samples from a population with density function f where fx 0 almost everywhere, everywhere continuous and has certain integral properties. For populations where f does not have these integral properties, this joint density is an approximation. This joint density function is used to derive the density function of the t-statistic for samples from f. The family of generalized normal density functions is used for an example. The approximation for the t-density is given for that family. For some specific members of the family, the true probabilities for the approximations are tabled.
- Statistics and Probability