## Brazilian Journal of Probability and Statistics

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

### A new weighted Lindley distribution with application

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

#### Abstract

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

**Source**

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

**Dates**

Received: April 2014

Accepted: June 2014

First available in Project Euclid: 19 January 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1453211800

**Digital Object Identifier**

doi:10.1214/14-BJPS253

**Mathematical Reviews number (MathSciNet)**

MR3453512

**Zentralblatt MATH identifier**

1381.62038

**Keywords**

Estimation Gini index skewness weighted distributions

#### Citation

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. https://projecteuclid.org/euclid.bjps/1453211800