An Exact Expression for the Behrens-Fisher Distribution with Applications

Charles W. Champ, Fengjiao Hu

Research output: Contribution to book or proceedingConference articlepeer-review

Abstract

An exact solution is given for the Behrens-Fisher distribution under the independent Normal model. The cumulative distribution function (cdf) and the probability density function (pdf) are expressed as convex combinations of non-central t-distributions cdfs and pdfs, respectively. It is then observed that if the means are equal the distribution depends only on the ratio of the two population variances and the sample sizes. When the means are not equal, the distribution depends on the difference of the two means, the ratio of the two population variances, and the two sample sizes. Some examples are given applying these results.

Original languageEnglish
Title of host publicationApplied Mathematical Analysis and Computations II - 1st SGMC
EditorsDivine Wanduku, Shijun Zheng, Zhan Chen, Andrew Sills, Haomin Zhou, Ephraim Agyingi
PublisherSpringer
Pages227-245
Number of pages19
ISBN (Print)9783031697098
DOIs
StatePublished - 2024
Event1st Southern Georgia Mathematics Conference, SGMC 2021 - Virtual, Online
Duration: Apr 2 2021Apr 3 2021

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume472
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference1st Southern Georgia Mathematics Conference, SGMC 2021
CityVirtual, Online
Period04/2/2104/3/21

Scopus Subject Areas

  • General Mathematics

Keywords

  • Cumulative distribution function
  • Non-central t distribution
  • Probability density function

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