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May 2016 Log-symmetric distributions: Statistical properties and parameter estimation
Luis Hernando Vanegas, Gilberto A. Paula
Braz. J. Probab. Stat. 30(2): 196-220 (May 2016). DOI: 10.1214/14-BJPS272


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.


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Luis Hernando Vanegas. Gilberto A. Paula. "Log-symmetric distributions: Statistical properties and parameter estimation." Braz. J. Probab. Stat. 30 (2) 196 - 220, May 2016.


Received: 1 March 2014; Accepted: 1 November 2014; Published: May 2016
First available in Project Euclid: 31 March 2016

zbMATH: 1381.60047
MathSciNet: MR3481101
Digital Object Identifier: 10.1214/14-BJPS272

Keywords: Asymmetric distributions , Bayesian analysis , log-location-scale lifetime models , Robust estimates , skewness

Rights: Copyright © 2016 Brazilian Statistical Association


Vol.30 • No. 2 • May 2016
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