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Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution

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  • Daan de Waal

    (Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
    Department of Mathematical Statistics and Actuarial Science, University of Free State, Bloemfontein 9301, South Africa
    These authors contributed equally to this work.)

  • Tristan Harris

    (Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
    These authors contributed equally to this work.)

  • Alta de Waal

    (Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
    Centre for Artificial Intelligence Research, Cape Town, South Africa
    These authors contributed equally to this work.)

  • Jocelyn Mazarura

    (Department of Statistics, University of Pretoria, Pretoria 0002, South Africa
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Daan de Waal & Tristan Harris & Alta de Waal & Jocelyn Mazarura, 2022. "Modelling Bimodal Data Using a Multivariate Triangular-Linked Distribution," Mathematics, MDPI, vol. 10(14), pages 1-20, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2370-:d:856928
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    References listed on IDEAS

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