A comparison study on a new five-parameter generalized Lindley distribution with its sub-models


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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability


ISSN: 1234-7655
eISSN: 2450-0291





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VOLUME 21 , ISSUE 2 (June 2020) > List of articles

A comparison study on a new five-parameter generalized Lindley distribution with its sub-models

Ramajeyam Tharshan / Pushpakanthie Wijekoon

Keywords : Lindley distribution, mixture distributions, size-biased distributions, maximum likelihood estimation

Citation Information : Statistics in Transition New Series. Volume 21, Issue 2, Pages 89-117, DOI: https://doi.org/10.21307/stattrans-2020-015

License : (CC BY-NC-ND 4.0)

Received Date : 28-August-2019 / Accepted: 12-March-2020 / Published Online: 01-June-2020



In recent years, modifications of the classical Lindley distribution have been considered by many authors. In this paper, we introduce a new generalization of the Lindley distribution based on a mixture of exponential and gamma distributions with different mixing proportions and compare its performance with its sub-models. The new distribution accommodates the classical Lindley, Quasi Lindley, Two-parameter Lindley, Shanker, Lindley distribution with location parameter, and Three-parameter Lindley distributions as special cases. Various structural properties of the new distribution are discussed and the size-biased and the length-biased are derived. A simulation study is conducted to examine the mean square error for the parameters by means of the method of maximum likelihood. Finally, simulation studies and some real-world data sets are used to illustrate its flexibility in terms of its location, scale and shape parameters.

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