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

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.