The γ-order generalized chi-square distribution

Based on the definition of the γ-order generalized normal, the γ-order generalized standard normal is obtained, and applications are referred. We proceed on the definition of the γ-order generalized chi-square, [Formula: see text] and the probability density function (pdf) is evaluated. Moreover, th...

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Main Authors: Christos P. Kitsos, Ioannis S. Stamatiou
Format: Article
Language:English
Published: Taylor & Francis 2024-12-01
Series:Research in Statistics
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Online Access:https://www.tandfonline.com/doi/10.1080/27684520.2024.2377684
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author Christos P. Kitsos
Ioannis S. Stamatiou
author_facet Christos P. Kitsos
Ioannis S. Stamatiou
author_sort Christos P. Kitsos
collection DOAJ
description Based on the definition of the γ-order generalized normal, the γ-order generalized standard normal is obtained, and applications are referred. We proceed on the definition of the γ-order generalized chi-square, [Formula: see text] and the probability density function (pdf) is evaluated. Moreover, the moment generating function (mgf) of the [Formula: see text] is evaluated and in the case of γ = 2 the mgf of the well known [Formula: see text] is obtained. The same procedure is followed for the moments of the [Formula: see text] One step forward is the evaluation of the convolution of two [Formula: see text] and therefore [Formula: see text] is obtained eventually and the corresponding pdf is evaluated. Finally examples and applications of [Formula: see text] are discussed.
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spelling doaj-art-4c1d70364c77445e8f5d7b2875a110152025-08-20T02:50:56ZengTaylor & FrancisResearch in Statistics2768-45202024-12-012110.1080/27684520.2024.2377684The γ-order generalized chi-square distributionChristos P. Kitsos0Ioannis S. Stamatiou1Department of Informatics, University of West Attica, Athens, GreeceDepartment of Surveying and Geoinformatics Engineering, University of West Attica, Athens, GreeceBased on the definition of the γ-order generalized normal, the γ-order generalized standard normal is obtained, and applications are referred. We proceed on the definition of the γ-order generalized chi-square, [Formula: see text] and the probability density function (pdf) is evaluated. Moreover, the moment generating function (mgf) of the [Formula: see text] is evaluated and in the case of γ = 2 the mgf of the well known [Formula: see text] is obtained. The same procedure is followed for the moments of the [Formula: see text] One step forward is the evaluation of the convolution of two [Formula: see text] and therefore [Formula: see text] is obtained eventually and the corresponding pdf is evaluated. Finally examples and applications of [Formula: see text] are discussed.https://www.tandfonline.com/doi/10.1080/27684520.2024.2377684γ-order generalized normal distributionchi-square distributionmoment generating functionlaplace transformation
spellingShingle Christos P. Kitsos
Ioannis S. Stamatiou
The γ-order generalized chi-square distribution
Research in Statistics
γ-order generalized normal distribution
chi-square distribution
moment generating function
laplace transformation
title The γ-order generalized chi-square distribution
title_full The γ-order generalized chi-square distribution
title_fullStr The γ-order generalized chi-square distribution
title_full_unstemmed The γ-order generalized chi-square distribution
title_short The γ-order generalized chi-square distribution
title_sort γ order generalized chi square distribution
topic γ-order generalized normal distribution
chi-square distribution
moment generating function
laplace transformation
url https://www.tandfonline.com/doi/10.1080/27684520.2024.2377684
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