A Family of Truncated Positive Distributions

Héctor J. Gómez, Karol I. Santoro, Inmaculada Barranco-Chamorro, Osvaldo Venegas (), Diego I. Gallardo and Héctor W. Gómez
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Héctor J. Gómez: Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
Karol I. Santoro: Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Inmaculada Barranco-Chamorro: Departamento de Estadística e Investigación Operativa, Facultad de Matemáticas, Universidad de Sevilla, 41012 Sevilla, Spain
Osvaldo Venegas: Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
Diego I. Gallardo: Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
Héctor W. Gómez: Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile

Mathematics, 2023, vol. 11, issue 21, 1-15

Abstract: In this paper, a new family of continuous distributions with positive support is introduced. This family is generated by a truncation of the family of univariate symmetrical distributions. In this new family of distributions, general properties, such as moments, asymmetry and kurtosis coefficients, are derived. Particular cases of interest based on the normal, logistic, Laplace and Cauchy models are discussed in depth. The estimation of parameters is carried out by applying moments and maximum likelihood methods. Also, a simulation study was conducted to illustrate the good performance of estimators. An application to the Survival Times (in days) of Guinea Pigs dataset is included, where the special cases of distributions in this family are fitted. The option which provides the best fit is ultimately chosen. An R package, called “tpn”, has been implemented, which includes the relevant cases of interest in this family.

Keywords: positive truncation; likelihood; symmetric distributions; tpn package (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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