A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data

Karol I. Santoro, Diego I. Gallardo, Osvaldo Venegas (), Isaac E. Cortés and Héctor W. Gómez
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Karol I. Santoro: Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
Diego I. Gallardo: Departamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, Chile
Osvaldo Venegas: Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile
Isaac E. Cortés: Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos 13560-095, Brazil
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 22, 1-15

Abstract: In this paper, we extend the Lomax–Rayleigh distribution to increase its kurtosis. The construction of this distribution is based on the idea of the Slash distribution, that is, its representation is based on the quotient of two independent random variables, one being a random variable with a Lomax–Rayleigh distribution and the other a beta ( q , 1 ) . Based on the representation of this family, we study its basic properties, such as moments, coefficients of skewness, and kurtosis. We perform statistical inference using the methods of moments and maximum likelihood. To illustrate this methodology, we apply it to two real data sets.

Keywords: Slash distribution; Lomax–Rayleigh distribution; kurtosis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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