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The Truncated Cauchy Power Family of Distributions with Inference and Applications

As a matter of fact, the statistical literature lacks of general family of distributions based on the truncated Cauchy distribution. In this paper, such a family is proposed, called the truncated Cauchy power-G family. It stands out for the originality of the involved functions, its overall simplici...

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Autores principales: Aldahlan, Maha A., Jamal, Farrukh, Chesneau, Christophe, Elgarhy, Mohammed, Elbatal, Ibrahim
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516817/
https://www.ncbi.nlm.nih.gov/pubmed/33286120
http://dx.doi.org/10.3390/e22030346
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author Aldahlan, Maha A.
Jamal, Farrukh
Chesneau, Christophe
Elgarhy, Mohammed
Elbatal, Ibrahim
author_facet Aldahlan, Maha A.
Jamal, Farrukh
Chesneau, Christophe
Elgarhy, Mohammed
Elbatal, Ibrahim
author_sort Aldahlan, Maha A.
collection PubMed
description As a matter of fact, the statistical literature lacks of general family of distributions based on the truncated Cauchy distribution. In this paper, such a family is proposed, called the truncated Cauchy power-G family. It stands out for the originality of the involved functions, its overall simplicity and its desirable properties for modelling purposes. In particular, (i) only one parameter is added to the baseline distribution avoiding the over-parametrization phenomenon, (ii) the related probability functions (cumulative distribution, probability density, hazard rate, and quantile functions) have tractable expressions, and (iii) thanks to the combined action of the arctangent and power functions, the flexible properties of the baseline distribution (symmetry, skewness, kurtosis, etc.) can be really enhanced. These aspects are discussed in detail, with the support of comprehensive numerical and graphical results. Furthermore, important mathematical features of the new family are derived, such as the moments, skewness and kurtosis, two kinds of entropy and order statistics. For the applied side, new models can be created in view of fitting data sets with simple or complex structure. This last point is illustrated by the consideration of the Weibull distribution as baseline, the maximum likelihood method of estimation and two practical data sets wit different skewness properties. The obtained results show that the truncated Cauchy power-G family is very competitive in comparison to other well implanted general families.
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spelling pubmed-75168172020-11-09 The Truncated Cauchy Power Family of Distributions with Inference and Applications Aldahlan, Maha A. Jamal, Farrukh Chesneau, Christophe Elgarhy, Mohammed Elbatal, Ibrahim Entropy (Basel) Article As a matter of fact, the statistical literature lacks of general family of distributions based on the truncated Cauchy distribution. In this paper, such a family is proposed, called the truncated Cauchy power-G family. It stands out for the originality of the involved functions, its overall simplicity and its desirable properties for modelling purposes. In particular, (i) only one parameter is added to the baseline distribution avoiding the over-parametrization phenomenon, (ii) the related probability functions (cumulative distribution, probability density, hazard rate, and quantile functions) have tractable expressions, and (iii) thanks to the combined action of the arctangent and power functions, the flexible properties of the baseline distribution (symmetry, skewness, kurtosis, etc.) can be really enhanced. These aspects are discussed in detail, with the support of comprehensive numerical and graphical results. Furthermore, important mathematical features of the new family are derived, such as the moments, skewness and kurtosis, two kinds of entropy and order statistics. For the applied side, new models can be created in view of fitting data sets with simple or complex structure. This last point is illustrated by the consideration of the Weibull distribution as baseline, the maximum likelihood method of estimation and two practical data sets wit different skewness properties. The obtained results show that the truncated Cauchy power-G family is very competitive in comparison to other well implanted general families. MDPI 2020-03-17 /pmc/articles/PMC7516817/ /pubmed/33286120 http://dx.doi.org/10.3390/e22030346 Text en © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Aldahlan, Maha A.
Jamal, Farrukh
Chesneau, Christophe
Elgarhy, Mohammed
Elbatal, Ibrahim
The Truncated Cauchy Power Family of Distributions with Inference and Applications
title The Truncated Cauchy Power Family of Distributions with Inference and Applications
title_full The Truncated Cauchy Power Family of Distributions with Inference and Applications
title_fullStr The Truncated Cauchy Power Family of Distributions with Inference and Applications
title_full_unstemmed The Truncated Cauchy Power Family of Distributions with Inference and Applications
title_short The Truncated Cauchy Power Family of Distributions with Inference and Applications
title_sort truncated cauchy power family of distributions with inference and applications
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7516817/
https://www.ncbi.nlm.nih.gov/pubmed/33286120
http://dx.doi.org/10.3390/e22030346
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