On the estimation of stress strength reliability parameter of inverted exponential distribution

Abstract

This paper aims to estimate the stress-strength reliability parameter R = P (Y < X), when X and Y are independent inverted exponential random variable. We have also disscused some fundamental properties of the considered distribution. The maximum likelihood estimator (MLE) of R and its asymptotic distribution are obtained. The Bayesian estimation of the reliability parameter has been also discussed under the assumption of independent gamma prior. Numerical integration technique is used for Bayesian computation. The proposed estimators are compared in terms of their mean squared errors through the simulation study. Two real data sets representing survival of head and neck cancer patients are fitted using the inverted exponential distribution and used to estimate the stress-strength parameters and reliability.

Bayesian Estimation under Different Loss Functions Using Gamma Prior for the Case of Exponential Distribution

“…We have studied this under gamma prior for exponential distribution to see the comparative situation. We can use the exponential distribution to estimate the stress-strength parameters and reliability of representing survival of head and neck cancer patients [8].…”

Bivariate general exponential models with stress-strength reliability application

“…We will denote the bivariate distribution with survival function having the form (4) by BEF(θ 0 , θ 1 , θ 2 ; c). Clearly, X and Y are independent if and only if (iff) θ 0 = 0.…”

“…In the area of stress-strength models, there have been a large amount of work regarding estimation of the reliability parameter, R = P(Y < X), when X and Y independent random variables belonging to the same univariate family, see for example Mokhlis [2], Kundu and Gupta [3], Singh et al [4] and others. Recently, Mokhlis et al [1] discussed R, when the variables are independent with survival functions having forms (1) and (2), respectively.…”

On the estimation of stress strength reliability parameter of inverted gamma distribution

“…The data are corresponded to the survival times of 51 patients in one group were treated using radiotherapy (X), whereas the 45 patients belonging to other group were treated using a combined radiotherapy and chemotherapy (Y). The data sets given as follows Recently Singh et al [19] is modelled this data using inverted exponential distribution(IED), inverse Rayleigh distribution (IRD) and generalized inverted exponential distribution (GIED). Also Makkar et al [15] is modelled the data using log-normal distribution (LN) and considered Bayesian survival analysis.…”

“…Some of the recent work on the stress-strength model can be seen in [13,[16][17][18]. Recently Singh et al [19] consider the estimation of the parameter R when X and Y are independent inverted exponential random variables.…”