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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...
Autores principales: | , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2020
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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. |
format | Online Article Text |
id | pubmed-7516817 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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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