## Brazilian Journal of Probability and Statistics

### The beta log-logistic distribution

Artur J. Lemonte

#### 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

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

Digital Object Identifier
doi:10.1214/12-BJPS209

Mathematical Reviews number (MathSciNet)
MR3263050

Zentralblatt MATH identifier
1312.60008

#### 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

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