New Families of Bivariate Copulas via Unit Lomax Distortion
This article studies a new family of bivariate copulas constructed using the unit-Lomax distortion derived from a transformation of the non-negative Lomax random variable into a variable whose support is the unit interval. Existing copulas play the role of the base copulas that are distorted into ne...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Risks |
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| Online Access: | https://www.mdpi.com/2227-9091/8/4/106 |
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| author | Fadal Abdullah-A Aldhufairi Ranadeera G.M. Samanthi Jungsywan H. Sepanski |
| author_facet | Fadal Abdullah-A Aldhufairi Ranadeera G.M. Samanthi Jungsywan H. Sepanski |
| author_sort | Fadal Abdullah-A Aldhufairi |
| collection | DOAJ |
| description | This article studies a new family of bivariate copulas constructed using the unit-Lomax distortion derived from a transformation of the non-negative Lomax random variable into a variable whose support is the unit interval. Existing copulas play the role of the base copulas that are distorted into new families of copulas with additional parameters, allowing more flexibility and better fit to data. We present general forms for the new bivariate copula function and its conditional and density distributions. The properties of the new family of the unit-Lomax induced copulas, including the tail behaviors, limiting cases in parameters, Kendall’s tau, and concordance order, are investigated for cases when the base copulas are Archimedean, such as the Clayton, Gumbel, and Frank copulas. An empirical application of the proposed copula model is presented. The unit-Lomax distorted copula models outperform the base copulas. |
| first_indexed | 2024-03-10T15:38:42Z |
| format | Article |
| id | doaj.art-909c55801f814de1913c41efc034739a |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-03-10T15:38:42Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-909c55801f814de1913c41efc034739a2023-11-20T16:59:42ZengMDPI AGRisks2227-90912020-10-018410610.3390/risks8040106New Families of Bivariate Copulas via Unit Lomax DistortionFadal Abdullah-A Aldhufairi0Ranadeera G.M. Samanthi1Jungsywan H. Sepanski2Department of Statistics, Actuarial and Data Sciences, Central Michigan University, Mount Pleasant, MI 48859, USADepartment of Statistics, Actuarial and Data Sciences, Central Michigan University, Mount Pleasant, MI 48859, USADepartment of Statistics, Actuarial and Data Sciences, Central Michigan University, Mount Pleasant, MI 48859, USAThis article studies a new family of bivariate copulas constructed using the unit-Lomax distortion derived from a transformation of the non-negative Lomax random variable into a variable whose support is the unit interval. Existing copulas play the role of the base copulas that are distorted into new families of copulas with additional parameters, allowing more flexibility and better fit to data. We present general forms for the new bivariate copula function and its conditional and density distributions. The properties of the new family of the unit-Lomax induced copulas, including the tail behaviors, limiting cases in parameters, Kendall’s tau, and concordance order, are investigated for cases when the base copulas are Archimedean, such as the Clayton, Gumbel, and Frank copulas. An empirical application of the proposed copula model is presented. The unit-Lomax distorted copula models outperform the base copulas.https://www.mdpi.com/2227-9091/8/4/106Archimedean copuladistortionKendall’s taulomax distributiontail dependence |
| spellingShingle | Fadal Abdullah-A Aldhufairi Ranadeera G.M. Samanthi Jungsywan H. Sepanski New Families of Bivariate Copulas via Unit Lomax Distortion Risks Archimedean copula distortion Kendall’s tau lomax distribution tail dependence |
| title | New Families of Bivariate Copulas via Unit Lomax Distortion |
| title_full | New Families of Bivariate Copulas via Unit Lomax Distortion |
| title_fullStr | New Families of Bivariate Copulas via Unit Lomax Distortion |
| title_full_unstemmed | New Families of Bivariate Copulas via Unit Lomax Distortion |
| title_short | New Families of Bivariate Copulas via Unit Lomax Distortion |
| title_sort | new families of bivariate copulas via unit lomax distortion |
| topic | Archimedean copula distortion Kendall’s tau lomax distribution tail dependence |
| url | https://www.mdpi.com/2227-9091/8/4/106 |
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