Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution

Daan de Waal, Tristan Harris, Alta de Waal and Jocelyn Mazarura
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Daan de Waal: Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
Tristan Harris: Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
Alta de Waal: Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
Jocelyn Mazarura: Department of Statistics, University of Pretoria, Pretoria 0002, South Africa

Mathematics, 2022, vol. 10, issue 14, 1-20

Abstract: 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.

Keywords: bimodality; triangular distributions; random generation; copulas; mixture models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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