Testing a Point Null Hypothesis against One-Sided for Non Regular and Exponential Families: The Reconcilability Condition to P-values and Posterior Probability
نویسندگان
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.
doi
10.52547/jirss.19.2.101چکیده
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.
