Brazilian Journal of Probability and Statistics

A new weighted Lindley distribution with application

A. Asgharzadeh, Hassan S. Bakouch, S. Nadarajah, and F. Sharafi

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The Lindley distribution has been generalized by many authors in recent years. Here, we introduce a new generalization that provides better fits than the Lindley distribution and all of its known generalizations. The distribution contains Lindley and weighted Lindley (Ghitany et al. (Math. Comput. Simulation 81 (2011) 1190–1201)) distributions as special cases. Also, the distribution can be represented as a mixture of weighted exponential (Gupta and Kundu (Statistics 43 (2009) 621–634)) and weighted gamma distributions, and as a negative mixture of Lindley distributions with different parameters. Various properties of the distribution (including quantiles, moments, moment generating function, hazard rate function, mean residual lifetime, Lorenz curve, Gini index, Rényi entropy and Mathai–Haubold entropy) are derived. Maximum likelihood estimators of the distribution parameters are derived and their behavior is assessed via simulation. Fisher’s information matrix and asymptotic confidence intervals for the distribution parameters are given. Finally, a real data application is presented.

Article information

Braz. J. Probab. Stat., Volume 30, Number 1 (2016), 1-27.

Received: April 2014
Accepted: June 2014
First available in Project Euclid: 19 January 2016

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Zentralblatt MATH identifier

Estimation Gini index skewness weighted distributions


Asgharzadeh, A.; Bakouch, Hassan S.; Nadarajah, S.; Sharafi, F. A new weighted Lindley distribution with application. Braz. J. Probab. Stat. 30 (2016), no. 1, 1--27. doi:10.1214/14-BJPS253.

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