Annals of Data Science

, Volume 6, Issue 4, pp 707–736 | Cite as

Generalized Lindley Distribution Based on Order Statistics and Associated Inference with Application

  • Devendra KumarEmail author
  • Anju Goyal


The generalized Lindley distribution is an important distribution for analyzing the stress–strength reliability models and lifetime data, which is quite flexible and can be used effectively in modeling survival data. It can have increasing, decreasing, upside-down bathtub and bathtub shaped failure rate. In this paper, we derive the exact explicit expressions for the single, double (product), triple and quadruple moments of order statistics from the generalized Lindley distribution. 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. Also, 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.


Generalized Lindley distribution Order statistics Single moment Double moment Type-II right censoring Best linear unbiased estimator 



The authors would like to thank the editor and the referee for careful reading and comments which greatly improved the article.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsCentral University of HaryanaMahendragarhIndia
  2. 2.Department of StatisticsPanjab UniversityChandigarhIndia

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