On a family of discrete log-symmetric distributions

TL;DR

This paper introduces a new class of discrete, asymmetric distributions derived from continuous log-symmetric distributions, addressing the limitations of using continuous models for discrete data.

Contribution

It proposes a novel family of discrete distributions, discusses their properties, and evaluates maximum likelihood estimation through simulations and real data examples.

Findings

Maximum likelihood estimators perform well in simulations

The new distributions effectively model discrete, asymmetric data

Methodology is validated with censored and uncensored datasets

Abstract

The use of continuous probability distributions has been widespread in problems with purely discrete nature. In general, such distributions are not appropriate in this scenario. In this paper, we introduce a class of discrete and asymmetric distributions based on the family of continuous log-symmetric distributions. Some properties are discussed as well as estimation by the maximum likelihood method. A Monte Carlo simulation study is carried out to evaluate the performance of the estimators, and censored and uncensored data sets are used to illustrate the proposed methodology.