## Brazilian Journal of Probability and Statistics

### Log-symmetric distributions: Statistical properties and parameter estimation

#### Abstract

In this paper, we study the main statistical properties of the class of log-symmetric distributions, which includes as special cases bimodal distributions as well as distributions that have heavier/lighter tails than those of the log-normal distribution. This family includes distributions such as the log-normal, log-Student-$t$, harmonic law, Birnbaum–Saunders, Birnbaum–Saunders-$t$ and generalized Birnbaum–Saunders. We derive quantile-based measures of location, dispersion, skewness, relative dispersion and kurtosis for the log-symmetric class that are appropriate in the context of asymmetric and heavy-tailed distributions. Additionally, we discuss parameter estimation based on both classical and Bayesian approaches. The usefulness of the log-symmetric class is illustrated through a statistical analysis of a real dataset, in which the performance of the log-symmetric class is compared with that of some competitive and very flexible distributions.

#### Article information

Source
Braz. J. Probab. Stat., Volume 30, Number 2 (2016), 196-220.

Dates
Accepted: November 2014
First available in Project Euclid: 31 March 2016

https://projecteuclid.org/euclid.bjps/1459429710

Digital Object Identifier
doi:10.1214/14-BJPS272

Mathematical Reviews number (MathSciNet)
MR3481101

Zentralblatt MATH identifier
1381.60047

#### Citation

Vanegas, Luis Hernando; Paula, Gilberto A. Log-symmetric distributions: Statistical properties and parameter estimation. Braz. J. Probab. Stat. 30 (2016), no. 2, 196--220. doi:10.1214/14-BJPS272. https://projecteuclid.org/euclid.bjps/1459429710

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