Bayesian Estimation of Stress Strength Reliability using Upper Record Values from Generalised Inverted Exponential Distribution

Ritu Kumari,Kalpana K Mahajan,Sangeeta Arora

doi:10.33889/ijmems.2019.4.4-070

Abstract

The paper develops Bayesian estimators and HPD intervals for the stress strength reliability of generalised inverted exponential distribution using upper record values. For prior distribution, informative prior as well as non-informative prior both are considered. The Bayes estimators are obtained under both symmetric and asymmetric loss functions. A simulation study is conducted to obtain the Bayes estimates of stress strength reliability. Simulated data sets are also considered here for illustration purpose.

Highlights

The exponential distribution is the most commonly used distribution in reliability field due to its simple form and a characteristic of constant hazard rate
Abouammoh and Alshinigiti (2009) pointed out that generalised inverted exponential distribution gives better fit than inverted exponential, gamma, weibull and generalised exponential distribution in many situations
The value of expected loss function and the length of highest posterior density (HPD) credible intervals decrease as the sample sizes increase (Tables 1 and 2)

Summary

Introduction

The exponential distribution is the most commonly used distribution in reliability field due to its simple form and a characteristic of constant hazard rate. Dey (2007) considered Bayesian estimations of the parameters of inverted exponential distribution under symmetric and asymmetric loss functions. A real life example using upper record values in case of generalised inverted exponential distribution is considered by Dey et al (2016). The thrust of this paper is Bayesian estimation of stress-strength reliability in the generalized inverted exponential distribution based on upper record values. This problem was studied by Hussian (2013) for ordinary samples from generalised inverted exponential distribution. 3. Bayesian Estimation Bayes estimators for stress strength reliability are derived using upper record values in case of both informative and non-informative priors under symmetric loss function (squared error loss function) and asymmetric loss function (generalised entropy loss function).

Bayesian Estimation of η = P(Y < X) Using Gamma Prior

Conclusion