Journal of the Iranian Statistical Society

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

Authors

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

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Journal of the Iranian Statistical Society
Volume 19, Issue 2
December 2020
Pages 101-117
  • Receive Date: 23 July 2022
  • Revise Date: 10 May 2024
  • Accept Date: 23 July 2022