Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA
The generalized half-logistic distribution is ideal to fit the lifetime of some products, such as ball bearings and electrical insulation. In this paper, we aim to extend this scope by creating a motivated bivariate version. We thus introduce the bivariate generalized half-logistic distribution usin...
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MDPI AG
2022-08-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/27/4/72 |
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| author | Marwa K. H. Hassan Christophe Chesneau |
| author_facet | Marwa K. H. Hassan Christophe Chesneau |
| author_sort | Marwa K. H. Hassan |
| collection | DOAJ |
| description | The generalized half-logistic distribution is ideal to fit the lifetime of some products, such as ball bearings and electrical insulation. In this paper, we aim to extend this scope by creating a motivated bivariate version. We thus introduce the bivariate generalized half-logistic distribution using the Farlie Gumbel Morgenstern (FGM) copula, which is called the FGM bivariate generalized half-logistic distribution (FGMBGHLD for short). In particular, the FGMBGHLD finds application in describing bivariate lifetime datasets that have weak correlations between variables. Some statistical properties and functions of our new distribution, such as the product moments, moment generating function, reliability function, and hazard rate function, are derived. We discuss the maximum likelihood estimation method of the FGMBGHLD parameters. As an application of the FGMBGHLD in reliability, we consider the stress–strength model when the stress and strength random variables are dependent. We also derive the point and interval estimates of the stress–strength coefficient. Finally, we use the data from the household income and expenditure survey of KSA 2018 for Saudi households by administrative region to demonstrate the practicability of the proposed model. A comparison with a modern bivariate Weibull distribution is performed. |
| first_indexed | 2024-03-09T04:07:42Z |
| format | Article |
| id | doaj.art-6053ca4a66ba4201bdd8272ead6e53c4 |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-09T04:07:42Z |
| publishDate | 2022-08-01 |
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| series | Mathematical and Computational Applications |
| spelling | doaj.art-6053ca4a66ba4201bdd8272ead6e53c42023-12-03T14:04:10ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472022-08-012747210.3390/mca27040072Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSAMarwa K. H. Hassan0Christophe Chesneau1Department of Mathematics, Faculty of Education, Ain Shams University, Cairo 11566, EgyptDepartment of Mathematics, LMNO, CNRS-Université de Caen, Campus II, Science 3, CEDEX, 14032 Caen, FranceThe generalized half-logistic distribution is ideal to fit the lifetime of some products, such as ball bearings and electrical insulation. In this paper, we aim to extend this scope by creating a motivated bivariate version. We thus introduce the bivariate generalized half-logistic distribution using the Farlie Gumbel Morgenstern (FGM) copula, which is called the FGM bivariate generalized half-logistic distribution (FGMBGHLD for short). In particular, the FGMBGHLD finds application in describing bivariate lifetime datasets that have weak correlations between variables. Some statistical properties and functions of our new distribution, such as the product moments, moment generating function, reliability function, and hazard rate function, are derived. We discuss the maximum likelihood estimation method of the FGMBGHLD parameters. As an application of the FGMBGHLD in reliability, we consider the stress–strength model when the stress and strength random variables are dependent. We also derive the point and interval estimates of the stress–strength coefficient. Finally, we use the data from the household income and expenditure survey of KSA 2018 for Saudi households by administrative region to demonstrate the practicability of the proposed model. A comparison with a modern bivariate Weibull distribution is performed.https://www.mdpi.com/2297-8747/27/4/72Farlie Gumbel Morgenstern (FGM) copulageneralized half-logistic distribution (GHLD)reliability parameterMonte Carlo simulationstatistical propertieshousehold financial affordability |
| spellingShingle | Marwa K. H. Hassan Christophe Chesneau Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA Mathematical and Computational Applications Farlie Gumbel Morgenstern (FGM) copula generalized half-logistic distribution (GHLD) reliability parameter Monte Carlo simulation statistical properties household financial affordability |
| title | Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA |
| title_full | Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA |
| title_fullStr | Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA |
| title_full_unstemmed | Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA |
| title_short | Bivariate Generalized Half-Logistic Distribution: Properties and Its Application in Household Financial Affordability in KSA |
| title_sort | bivariate generalized half logistic distribution properties and its application in household financial affordability in ksa |
| topic | Farlie Gumbel Morgenstern (FGM) copula generalized half-logistic distribution (GHLD) reliability parameter Monte Carlo simulation statistical properties household financial affordability |
| url | https://www.mdpi.com/2297-8747/27/4/72 |
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