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Inferences on stress-strength reliability from Lindley distributions. (English) Zbl 1294.62036
Summary: This article deals with the estimation of the stress-strength parameter \(R=\mathrm{P}(Y<X)\) when \(X\) and \(Y\) are independent Lindley random variables with different shape parameters. The uniformly minimum variance unbiased estimator has explicit expression, however, its exact or asymptotic distribution is very difficult to obtain. The maximum likelihood estimator of the unknown parameter can also be obtained in explicit form. We obtain the asymptotic distribution of the maximum likelihood estimator and it can be used to construct confidence interval of \(R\). Different parametric bootstrap confidence intervals are also proposed. Bayes estimator and the associated credible interval based on independent gamma priors on the unknown parameters are obtained using Monte Carlo methods. Different methods are compared using simulations and one data analysis has been performed for illustrative purposes.

MSC:
62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62F40 Bootstrap, jackknife and other resampling methods
62F15 Bayesian inference
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