Higher order moments of order statistics from the Lindley distribution and associated inference

ABSTRACT

The Lindley distribution is an important distribution for analysing the stress–strength reliability models and lifetime data. In many ways, the Lindley distribution is a better model than that based on the exponential distribution. Order statistics arise naturally in many of such applications. In this paper, we derive the exact explicit expressions for the single, double (product), triple and quadruple moments of order statistics from the Lindley distribution. Then, we use these moments to obtain the best linear unbiased estimates (BLUEs) of the location and scale parameters based on Type-II right-censored samples. Next, we use these results to determine the mean, variance, and coefficients of skewness and kurtosis of some certain linear functions of order statistics to develop Edgeworth approximate confidence intervals of the location and scale Lindley parameters. 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.

KEYWORDS:

• Type-II right censoring
• best linear unbiased estimation
• approximate confidence interval
• coefficients of skewness and kurtosis
• Edgeworth approximation
• Monte Carlo simulation and pivotal quantities

Acknowledgements

The authors would like to thank the referees for their helpful comments, which improved the presentation of the paper. Also, The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding this Research group no (RG-1435-056).

Disclosure statement

No potential conflict of interest was reported by the authors.