Estimation of the stress-strength parameter R=P(X>Y) in power Lindley distribution based on upper record values

In the literature, statistical estimation of the stress-strength reliability parameter R=P(X>Y) has attracted enormous interest. Recently, Ghitany et al. [7] studied statistical estimation of the parameter R in power Lindley distribution based on complete data sets. However, in practice, we may deal with record breaking data sets in which only values larger than the current extreme value are reported. In this paper, assuming that stress and strength random variables X and Y are independently distributed as power Lindley distribution, we consider estimation of the reliability parameter R based on upper record values. First, we obtain the maximum likelihood estimate of the reliability parameter and its asymptotic confidence interval. Then, considering squared error and Linex loss functions, we compute the Bayes estimates of R. Since, there are not closed forms for the Bayes estimates, we use Lindley method as well as a Markov Chain Monte Carlo procedure to obtain approximate Bayes estimates. In order to evaluate the performances of the proposed procedures, simulation studies are conducted. Finally, by analyzing real data sets, application of the proposed inferences using upper records is presented.