Bayesian Inference For Exponential Distribution Based On Upper Record Range

TL;DR

This paper develops Bayesian estimation methods for the exponential distribution's scale parameter using upper record range, including point and interval estimates, with applications of the Homotopy Perturbation Method and numerical validation.

Contribution

It introduces Bayesian point and interval estimators based on upper record range for exponential distribution, employing HPM and admissibility conditions, a novel approach in this context.

Findings

Bayesian estimators are derived for the exponential scale parameter.

HPM is effectively used to compute HPD intervals.

Numerical examples validate the proposed methods.

Abstract

This paper deals with Bayesian estimations of scale parameter of the exponential distribution based on upper record range (Rn). This has been done in two steps; point and interval. In the first step the quadratic, squared error and absolute error, loss functions have been considered to obtain Bayesian-point estimations. Also in the next step the shortest Bayes interval (Hight Posterior Density interval) and Bayes interval with equal tails based on upper record range have been found. Therefore, the Homotopy Perturbation Method(HPM) has been applied to obtain the limits of Hight Posterior Density intervals. Moreover, efforts have been made to meet the admissibility conditions for linear estimators based on upper record range of the form mRn+d by obtained Bayesian point estimations. So regarding the consideration of loss functions, the prior distribution between the conjunction family has been chosen to be able to produce the linear estimations from upper record range statistics. Finally, some numerical examples and simulations have been presented.