## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 28, Number 3 (2014), 313-332.

### The beta log-logistic distribution

#### Abstract

A new continuous distribution, so-called the beta log-logistic distribution, that extends the log-logistic distribution and some other distributions is proposed and studied. The new model is quite flexible to analyze positive data. Various structural properties of the new distribution are derived, including explicit expressions for the moments, mean deviations and Rényi and Shannon entropies. The score function is derived and the estimation of the model parameters is performed by maximum likelihood. We also determine the expected information matrix. The usefulness of the new model is illustrated by means of two real data sets. We hope that the new distribution proposed here will serve as an alternative model to other models available in the literature for modeling positive real data in many areas.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 28, Number 3 (2014), 313-332.

**Dates**

First available in Project Euclid: 17 July 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1405603504

**Digital Object Identifier**

doi:10.1214/12-BJPS209

**Mathematical Reviews number (MathSciNet)**

MR3263050

**Zentralblatt MATH identifier**

1312.60008

**Keywords**

Entropy fisk distribution log-logistic distribution maximum likelihood estimation mean deviations moments

#### Citation

Lemonte, Artur J. The beta log-logistic distribution. Braz. J. Probab. Stat. 28 (2014), no. 3, 313--332. doi:10.1214/12-BJPS209. https://projecteuclid.org/euclid.bjps/1405603504