Inferences for Modified Lindley Distribution Under Order Statistics with Applications

In this study, we obtain relations for the moments of order statistics from the modified Lindley distribution without any restriction for the parameter. In addition, we use these moments to obtain the mean, variances, and covariances of order statistics from the modified Lindley distribution. In particular, we compare, through simulation study, the performance of the maximum likelihood estimation, ordinary and weighted least-squares estimation, percentile estimators, and Cramér–von Mises estimators. Finally, we apply the paper’s findings to some real data sets.