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.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1971
Accession Number
AD0725563

Entities

People

  • Raymond Clayton Sansing

Organizations

  • Southern Methodist University

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Bibliographies
  • Coefficients
  • Data Science
  • Identities
  • Information Science
  • Integrals
  • Intervals
  • Normal Distribution
  • Normality
  • Probability
  • Random Variables
  • Statistical Tests
  • Statistics
  • Surveys
  • Theorems
  • United States
  • United States Government

Fields of Study

  • Mathematics

Readers

  • Statistical inference.