Testing a Point Null Hypothesis against One-Sided for Non Regular and Exponential Families: The Reconcilability Condition to P-values and Posterior Probability

Authors
Parisa Zolfaghari 1
Rahim Chinipardaz 2
Jafar Esmaily 3
1 Department of Statistics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
2 Department of Statistics, Faculty of Mathematics and Computer Science, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
3 Department of Mathematics, Ahvaz Branch, Islamic Azad University, Ahvaz, Iran.
10.52547/jirss.19.2.101
Abstract
In this paper, the reconcilability between the P-value and the posterior probability in testing a point null hypothesis against the one-sided hypothesis is considered. Two essential families, non regular and exponential family of distributions, are studied. It was shown in a non regular family of distributions; in some cases, it is possible to find a prior distribution function under which P-value and posterior probability are achieved. However, in the exponential family of distributions, this agreement is based on the complete monotonicity of a function of hazard rate.
Keywords
Completely Monotone
Exponential Family of Distributions
Non Regular Family of Distributions
P-values
Posterior probability
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Journal of the Iranian Statistical Society
Volume 19, Issue 2
December 2020
Pages 101-117

  • Receive Date 23 July 2022