Order Statistics from the Power Lindley Distribution and Associated Inference with Application

Abstract

Power Lindley distribution has been proposed recently by Ghitany et al. (Comput Stat Data Anal 64:20–33, 2013) as a simple and useful reliability model for analysing lifetime data. This model provides more flexibility than the Lindley distribution in terms of the shape of the density and hazard rate functions as well as its skewness and kurtosis. For this distribution, exact explicit expressions for single moments, product moments, marginal moment generating functions and joint moment generating functions of each of these order statistics are derived. By using these relations, we have tabulated the expected values, second moments, variances and covariances of order statistics from samples of sizes up to 10 for various values of the parameters. In addition, we use these moments to obtain the best linear unbiased estimates of the location and scale parameters based on Type-II right-censored samples. In addition, we carry out some numerical illustrations through Monte Carlo simulations to show the usefulness of the findings. Finally, we apply the findings of the paper to some real data set.