Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution
Bimodal distributions have rarely been studied although they appear frequently in datasets. We develop a novel bimodal distribution based on the triangular distribution and then expand it to the multivariate case using a Gaussian copula. To determine the goodness of fit of the univariate model, we u...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2022-07-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/10/14/2370 |
| _version_ | 1797417197803405312 |
|---|---|
| author | Daan de Waal Tristan Harris Alta de Waal Jocelyn Mazarura |
| author_facet | Daan de Waal Tristan Harris Alta de Waal Jocelyn Mazarura |
| author_sort | Daan de Waal |
| collection | DOAJ |
| description | Bimodal distributions have rarely been studied although they appear frequently in datasets. We develop a novel bimodal distribution based on the triangular distribution and then expand it to the multivariate case using a Gaussian copula. To determine the goodness of fit of the univariate model, we use the Kolmogorov–Smirnov (KS) and Cramér–von Mises (CVM) tests. The contributions of this work are that a simplistic yet robust distribution was developed to deal with bimodality in data, a multivariate distribution was developed as a generalisation of this univariate distribution using a Gaussian copula, a comparison between parametric and semi-parametric approaches to modelling bimodality is given, and an R package called btld is developed from the workings of this paper. |
| first_indexed | 2024-03-09T06:15:20Z |
| format | Article |
| id | doaj.art-12e70a6734594cd5b89b2346ce0de530 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T06:15:20Z |
| publishDate | 2022-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-12e70a6734594cd5b89b2346ce0de5302023-12-03T11:53:14ZengMDPI AGMathematics2227-73902022-07-011014237010.3390/math10142370Modelling Bimodal Data Using a Multivariate Triangular-Linked DistributionDaan de Waal0Tristan Harris1Alta de Waal2Jocelyn Mazarura3Department of Statistics, University of Pretoria, Pretoria 0002, South AfricaDepartment of Statistics, University of Pretoria, Pretoria 0002, South AfricaDepartment of Statistics, University of Pretoria, Pretoria 0002, South AfricaDepartment of Statistics, University of Pretoria, Pretoria 0002, South AfricaBimodal distributions have rarely been studied although they appear frequently in datasets. We develop a novel bimodal distribution based on the triangular distribution and then expand it to the multivariate case using a Gaussian copula. To determine the goodness of fit of the univariate model, we use the Kolmogorov–Smirnov (KS) and Cramér–von Mises (CVM) tests. The contributions of this work are that a simplistic yet robust distribution was developed to deal with bimodality in data, a multivariate distribution was developed as a generalisation of this univariate distribution using a Gaussian copula, a comparison between parametric and semi-parametric approaches to modelling bimodality is given, and an R package called btld is developed from the workings of this paper.https://www.mdpi.com/2227-7390/10/14/2370bimodalitytriangular distributionsrandom generationcopulasmixture models |
| spellingShingle | Daan de Waal Tristan Harris Alta de Waal Jocelyn Mazarura Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution Mathematics bimodality triangular distributions random generation copulas mixture models |
| title | Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution |
| title_full | Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution |
| title_fullStr | Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution |
| title_full_unstemmed | Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution |
| title_short | Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution |
| title_sort | modelling bimodal data using a multivariate triangular linked distribution |
| topic | bimodality triangular distributions random generation copulas mixture models |
| url | https://www.mdpi.com/2227-7390/10/14/2370 |
| work_keys_str_mv | AT daandewaal modellingbimodaldatausingamultivariatetriangularlinkeddistribution AT tristanharris modellingbimodaldatausingamultivariatetriangularlinkeddistribution AT altadewaal modellingbimodaldatausingamultivariatetriangularlinkeddistribution AT jocelynmazarura modellingbimodaldatausingamultivariatetriangularlinkeddistribution |