Abstract

This paper investigates Bayesian estimation techniques for deriving parameters of the Power Function Distribution (PFD) through the utilization of Ranked Set Sampling (RSS). We present both maximum likelihood and Bayesian approaches for parameter estimation employing RSS. Additionally, we establish asymptotic and bootstrap confidence intervals for the parameters. Bayesian estimators are computed utilizing squared error loss functions, weighted squared error loss functions, and M/Q squared error loss functions employing the Lindley approximation and importance sampling techniques. Furthermore, we forecast future samples based on RSS. Finally, we conduct reliability simulations to compare all proposed Bayesian estimation methods and analyze a real dataset for illustrative purposes.

Author: E.I. Abdul-Sathar and Sathya Reji

Received on: June, 2022

Accepted on: June, 2024