A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data
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–...
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MDPI AG
2023-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/22/4626 |
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| author | Karol I. Santoro Diego I. Gallardo Osvaldo Venegas Isaac E. Cortés Héctor W. Gómez |
| author_facet | Karol I. Santoro Diego I. Gallardo Osvaldo Venegas Isaac E. Cortés Héctor W. Gómez |
| author_sort | Karol I. Santoro |
| collection | DOAJ |
| description | 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<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. 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. |
| first_indexed | 2024-03-09T16:38:16Z |
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| language | English |
| last_indexed | 2024-03-09T16:38:16Z |
| publishDate | 2023-11-01 |
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| series | Mathematics |
| spelling | doaj.art-7cabc15970744c5b9309581f3595552a2023-11-24T14:54:15ZengMDPI AGMathematics2227-73902023-11-011122462610.3390/math11224626A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical DataKarol I. Santoro0Diego I. Gallardo1Osvaldo Venegas2Isaac E. Cortés3Héctor W. Gómez4Departamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileDepartamento de Estadística, Facultad de Ciencias, Universidad del Bío-Bío, Concepción 4081112, ChileDepartamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, ChileInstituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, São Carlos 13560-095, BrazilDepartamento de Estadística y Ciencias de Datos, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, ChileIn 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<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>,</mo><mn>1</mn><mo>)</mo></mrow></semantics></math></inline-formula>. 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.https://www.mdpi.com/2227-7390/11/22/4626Slash distributionLomax–Rayleigh distributionkurtosis |
| spellingShingle | Karol I. Santoro Diego I. Gallardo Osvaldo Venegas Isaac E. Cortés Héctor W. Gómez A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data Mathematics Slash distribution Lomax–Rayleigh distribution kurtosis |
| title | A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data |
| title_full | A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data |
| title_fullStr | A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data |
| title_full_unstemmed | A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data |
| title_short | A Heavy-Tailed Distribution Based on the Lomax–Rayleigh Distribution with Applications to Medical Data |
| title_sort | heavy tailed distribution based on the lomax rayleigh distribution with applications to medical data |
| topic | Slash distribution Lomax–Rayleigh distribution kurtosis |
| url | https://www.mdpi.com/2227-7390/11/22/4626 |
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