Bayesian Interval Estimation for the Two-Parameter Exponential Distribution Based on the Right Type II Censored Sample

Shu-Fei Wu

doi:10.3390/sym14020352

Abstract

The Bayesian interval estimation of the scale parameter for two-parameter exponential distribution is proposed based on the right type II censored sample. Under this type of censoring, two methods of Bayesian joint confidence region of the two parameters are also proposed. The simulation results show that the Bayesian method has a higher coverage probability than the existing method, so the Bayesian method is recommended for use. This research is related to the topic of asymmetrical probability distributions and applications across disciplines. The predictive interval of the future observation based on the right type II censored sample is also provided. One biometrical example is given to illustrate the proposed methods for the Bayesian interval estimations and prediction interval.

Highlights

Exponential Distribution Based on the Right Type II Censored Sample
Using a similar Bayesian approach in Wu and Chang [19], we propose the Bayesian joint confidence region for the two parameters of the two-parameter exponential distribution under right type II censoring
We recommend the users use Method 1 under (a,b) = (2,2) to construct the confidence region for two parameters based on the right type II censored sample

Summary

Introduction

Exponential Distribution Based on the Right Type II Censored Sample. The remaining s = n − m units of the item are removed and censored Many authors, such as Mann et al [5], Lawless [6] and Meeker and Escobar [7], have studied the estimation under type II censoring with different failure time distributions. Wu [8] proposed the interval estimation for the two-parameter exponential distribution based on the doubly type II censored sample. Wu [9] proposed the interval estimation for the Pareto distribution based on the doubly type II censored sample. In addition to the estimation of two parameters, the Bayesian predictive intervals of the future observation based on the right type II censored sample is derived.

Interval Estimation of Two Parameters

Simulation Study

A Biometrical Example

Conclusions