Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components
In this paper, we consider two finite mixture models (FMMs) with inverted-Kumaraswamy distributed components’ lifetimes. Several stochastic ordering results between the FMMs are obtained. Mainly, we focus on three different cases in terms of the heterogeneity of parameters. The usual stochastic orde...
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MDPI AG
2024-03-01
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| Online Access: | https://www.mdpi.com/2227-7390/12/6/852 |
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| author | Raju Bhakta Pradip Kundu Suchandan Kayal Morad Alizadeh |
| author_facet | Raju Bhakta Pradip Kundu Suchandan Kayal Morad Alizadeh |
| author_sort | Raju Bhakta |
| collection | DOAJ |
| description | In this paper, we consider two finite mixture models (FMMs) with inverted-Kumaraswamy distributed components’ lifetimes. Several stochastic ordering results between the FMMs are obtained. Mainly, we focus on three different cases in terms of the heterogeneity of parameters. The usual stochastic order between the FMMs is established when heterogeneity presents in one parameter as well as two parameters. In addition, we also study ageing faster order in terms of the reversed hazard rate between two FMMs when heterogeneity is in two parameters. For the case of heterogeneity in three parameters, we obtain the comparison results based on reversed hazard rate and likelihood ratio orders. The theoretical developments are illustrated using several examples and counterexamples. |
| first_indexed | 2024-04-24T18:02:56Z |
| format | Article |
| id | doaj.art-b46e2a7fa0644555b0832a85e5eac1ff |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-04-24T18:02:56Z |
| publishDate | 2024-03-01 |
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| series | Mathematics |
| spelling | doaj.art-b46e2a7fa0644555b0832a85e5eac1ff2024-03-27T13:53:06ZengMDPI AGMathematics2227-73902024-03-0112685210.3390/math12060852Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed ComponentsRaju Bhakta0Pradip Kundu1Suchandan Kayal2Morad Alizadeh3Department of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, Odisha, IndiaSchool of Computer Science and Engineering, XIM University, Bhubaneswar 752050, Odisha, IndiaDepartment of Mathematics, National Institute of Technology Rourkela, Rourkela 769008, Odisha, IndiaDepartment of Statistics, Faculty of Intelligent Systems Engineering and Data Science, Persian Gulf University, Bushehr 75169, IranIn this paper, we consider two finite mixture models (FMMs) with inverted-Kumaraswamy distributed components’ lifetimes. Several stochastic ordering results between the FMMs are obtained. Mainly, we focus on three different cases in terms of the heterogeneity of parameters. The usual stochastic order between the FMMs is established when heterogeneity presents in one parameter as well as two parameters. In addition, we also study ageing faster order in terms of the reversed hazard rate between two FMMs when heterogeneity is in two parameters. For the case of heterogeneity in three parameters, we obtain the comparison results based on reversed hazard rate and likelihood ratio orders. The theoretical developments are illustrated using several examples and counterexamples.https://www.mdpi.com/2227-7390/12/6/852FMMsstochastic ordersweak supermajorizationweak submajorizationmatrix majorization |
| spellingShingle | Raju Bhakta Pradip Kundu Suchandan Kayal Morad Alizadeh Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components Mathematics FMMs stochastic orders weak supermajorization weak submajorization matrix majorization |
| title | Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components |
| title_full | Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components |
| title_fullStr | Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components |
| title_full_unstemmed | Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components |
| title_short | Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components |
| title_sort | stochastic orderings between two finite mixtures with inverted kumaraswamy distributed components |
| topic | FMMs stochastic orders weak supermajorization weak submajorization matrix majorization |
| url | https://www.mdpi.com/2227-7390/12/6/852 |
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