Small Sample Equivalence Tests for Exponentiality


We consider small sample equivalence tests for exponentialy. Statistical inference in this setting is particularly challenging since equivalence testing procedures typically require much larger sample sizes, in comparison with classical "difference tests," to perform well. We make use of Butler's marginal likelihood for the shape parameter of a gamma distribution in our development of small sample equivalence tests for exponentiality. We consider two procedures using the principle of confidence interval inclusion, four Bayesian methods, and the uniformly most powerful unbiased (UMPU) test where a saddlepoint approximation to the intractable distribution of a canonical sufficient statistic is used. We perform small sample simulation studies to assess the bias of our various tests and show that all of the Bayes posteriors we consider are integrable. Our simulation studies show that the saddlepoint-approximated UMPU method performs remarkably well for small sample sizes and is the only method that consistently exhibits an empirical significance level close to the nominal 5% level.


Mathematics and Statistics

Keywords and Phrases

Bayesian networks; Equivalence classes; Equivalence tests; Exponentiality; Intractable distributions; Marginal likelihood; Saddle-point approximation; Statistical inference; Sufficient statistics; Uniformly most powerful tests; Statistical tests; Saddlepoint approximations

International Standard Serial Number (ISSN)

0361-0918; 1532-4141

Document Type

Article - Journal

Document Version


File Type





© 2018 Taylor & Francis, All rights reserved.

Publication Date

01 Jul 2018