Abstract
This paper deals with the problem of classical and Bayesian estimation of stress-strength reliability (R=P(X<Y)) based on upper record values from generalized inverted exponential distribution (GIED). Hassan {et al.} (2018) discussed the maximum likelihood estimator (MLE) and Bayes estimator of $R$ by considering that the scale parameter to be known for defined distribution while we consider the case when all the parameters of GIED are unknown. In the classical approach, we have discussed MLE and uniformly minimum variance estimator (UMVUE). In Bayesian approach, we have considered the Bays estimator of R by considering the squared error loss function. Further, based on upper records, we have considered the Asymptotic confidence interval based on MLE, Bayesian credible interval and bootstrap confidence interval for $R$. Finally, Monte Carlo simulations and real data applications are being carried out for comparing the performances of the estimators of R.
Highlights
For an extensive and lucid literature review regarding estimation and application of the stress-strength reliability, readers are referred to Johnson (1988) and Kotz et al (2003)
From Table-2, we observed that the EWCI for asymptotic distribution is less than the others and the coverage probability (CP) for the asymptotic distribution are less than the nominal level 0.95 while in other cases (MLE and bootstrap), CPs are greater than the nominal level 0.95
In this paper, we have obtained the maximum likelihood estimator (MLE), UMVUE and Bayesian estimator of R = P(X Y ) from generalized inverted exponential distribution (GIED) with a common scale and different shape parameters based on upper record values
Summary
Ghitany et al (2013) discussed the likelihood estimation for a general class of inverted exponential distribution based on complete and censored samples. Several researchers considered the estimation of the parameters of GIED based on complete, censored samples and record values. Estimation of parameters based on record values with different lifetime models have been discussed by various researchers. Estimation of stress-strength reliability based on record values has got more attention in last two decades. Baklizi (2008 a, 2014 a) has considered the MLE, associated CIs and Bayesian inference of stress-strength reliability using record values for the exponential distribution. Interval, bootstrap interval and interval using the generalized pivot variable) of the stressstrength reliability in two-parameter exponential distribution based on upper records has been obtained by Baklizi (2014 b). A real data example is presented in Section 7 for the purpose of illustration
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