A count distribution obtained as a discrete version of the continuous half-logistic distribution is introduced. It is derived by assigning to each non-negative integer value a probability proportional to the corresponding value of the density function of the parent model. Statistical properties of this new distribution, in particular related to its shape, moments, and reliability concepts, are described. Parameter estimation, which can be carried out resorting to different methods including maximum likelihood, is discussed and a numerical comparison between the methods, based on Monte Carlo simulations, is presented. The applicability of the proposed distribution is proved on a real dataset, which has been already fitted by other well-established count distributions. In order to increase the flexibility of this counting model, a generalization is finally suggested, which is obtained by adding a shape parameter to the continuous one-parameter half-logistic and then applying the same discretization technique, based on the mimicking of the density function.

A discrete analogue of the half-logistic distribution based on the mimicking of the probability density function / A. Barbiero. ((Intervento presentato al 4. convegno International Conference Mathematics Days in Sofia tenutosi a Sofia : July 10-14 nel 2023.

### A discrete analogue of the half-logistic distribution based on the mimicking of the probability density function

#### Abstract

A count distribution obtained as a discrete version of the continuous half-logistic distribution is introduced. It is derived by assigning to each non-negative integer value a probability proportional to the corresponding value of the density function of the parent model. Statistical properties of this new distribution, in particular related to its shape, moments, and reliability concepts, are described. Parameter estimation, which can be carried out resorting to different methods including maximum likelihood, is discussed and a numerical comparison between the methods, based on Monte Carlo simulations, is presented. The applicability of the proposed distribution is proved on a real dataset, which has been already fitted by other well-established count distributions. In order to increase the flexibility of this counting model, a generalization is finally suggested, which is obtained by adding a shape parameter to the continuous one-parameter half-logistic and then applying the same discretization technique, based on the mimicking of the density function.
##### Scheda breve Scheda completa Scheda completa (DC)
13-lug-2023
Settore SECS-S/01 - Statistica
Republic of Bulgaria - Ministry of Education and Science
Simons Foundation
PIKOM
Institute of Mathematics and Informatics of the Bulgarian Academy of Sciences
Union of the Bulgarian Mathematicians
Faculty of Mathematics and Informatics of Sofia University
https://mds.math.bas.bg/
A discrete analogue of the half-logistic distribution based on the mimicking of the probability density function / A. Barbiero. ((Intervento presentato al 4. convegno International Conference Mathematics Days in Sofia tenutosi a Sofia : July 10-14 nel 2023.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2434/1022390`