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.