An Alternative Discrete Analogue of the Half-Logistic Distribution Based on Minimization of a Distance between Cumulative Distribution Functions

Abstract

A discrete version of the continuous half-logistic distribution is introduced, which is based on the minimization of the Cramér distance between the corresponding continuous and step-wise cumulative distribution functions. The expression of the probability mass function is derived in an analytic form, and some properties of the distribution - mainly related to moments and reliability concepts - are discussed. As for sample estimation, three different techniques are suggested, whose theoretical and empirical features are examined also through a Monte Carlo simulation study, comprising several parameter and sample size combinations. A comparison is also made between the proposed distribution and a discrete version already proposed in the literature, based on a different rationale, and a main difference is highlighted. A count regression model is suggested where the response variable follows the discrete half-logistic distribution and artificial and real data are used to illustrate its use. Finally, the performance of the proposed distribution over other classical models is discussed based on a real data set.

KEYWORDS AND PHRASES:

• Count distribution
• Cramér distance
• cumulative distribution function
• logistic distribution
• survival data

Acknowledgments

The authors are thankful to the two anonymous referees for their comments, which helped to improve the manuscript’s quality. The corresponding author acknowledges “PSR Linea 2” 2021 funding from the Università degli Studi di Milano.

Disclosure Statement

No potential conflict of interest was reported by the author(s).