Presentation Title

An Exact Expression for the Behrens-Fisher Distribution with Applications

Location

Room 1909

Session Format

Paper Presentation

Research Area Topic:

Natural & Physical Sciences - Mathematics

Co-Presenters, Co- Authors, Co-Researchers, Mentors, or Faculty Advisors

Fengjiao Hu

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 infinite series 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 two population variances, and the two sample sizes. Methods are given for using the exact distribution to obtain an estimated confidence interval and an estimated p-value.

Keywords

Comparing two population means, Confidence interval, p-value, Welsh’s approximation

Presentation Type and Release Option

Presentation (Open Access)

Start Date

4-24-2015 1:30 PM

End Date

4-24-2015 2:30 PM

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Apr 24th, 1:30 PM Apr 24th, 2:30 PM

An Exact Expression for the Behrens-Fisher Distribution with Applications

Room 1909

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 infinite series 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 two population variances, and the two sample sizes. Methods are given for using the exact distribution to obtain an estimated confidence interval and an estimated p-value.