Chi-Square and Student Bridge Distributions and the Behrens–Fisher Statistic

Chi-Square and Student Bridge Distributions and the Behrens–Fisher Statistic

We prove that the Behrens–Fisher statistic follows a Student bridge distribution, the mixing coefficient of which depends on the two sample variances only through their ratio. To this end, it is first shown that a weighted sum of two independent normalized chi-square distributed random variables is...

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Bibliographic Details
Main Author: Wolf-Dieter Richter
Format: Article
Language:English
Published: MDPI AG 2020-08-01
Series:Stats
Subjects:
heteroscedasticity
unbalancedness
sums of weighted chi-squares
variance ratio
Welch approximation
three pillar bridges property
Online Access:https://www.mdpi.com/2571-905X/3/3/21

Internet

https://www.mdpi.com/2571-905X/3/3/21

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