The Density of the t-Statistic for Non-normal Distributions
Abstract
The joint density function of the sample mean and sample variance is recursively derived for samples from a population with density function f where f(x) > 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1971
- Accession Number
- AD0725563
Entities
People
- Raymond Clayton Sansing
Organizations
- Southern Methodist University