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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| Language: | English |
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Taylor & Francis
2024-12-01
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| 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. |
| format | Article |
| id | doaj-art-4c1d70364c77445e8f5d7b2875a11015 |
| institution | DOAJ |
| issn | 2768-4520 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Taylor & Francis |
| record_format | Article |
| series | Research in Statistics |
| 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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