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Introducing Two Parsimonious Standard Power Mixture Models for Bimodal Proportional Data with Application to Loss Given Default

Author

Listed:
  • Janette Larney

    (Centre for Business Mathematics and Informatics, North-West University, Potchefstroom 2531, South Africa
    These authors contributed equally to this work.)

  • Gerrit Lodewicus Grobler

    (School of Mathematical and Statistical Sciences, North-West University, Potchefstroom 2531, South Africa
    These authors contributed equally to this work.)

  • James Samuel Allison

    (School of Mathematical and Statistical Sciences, North-West University, Potchefstroom 2531, South Africa
    These authors contributed equally to this work.)

Abstract

The need to model proportional data is common in a range of disciplines however, due to its bimodal nature, U- or J-shaped data present a particular challenge. In this study, two parsimonious mixture models are proposed to accurately characterise this proportional U- and J-shaped data. The proposed models are applied to loss given default data, an application area where specific importance is attached to the accuracy with which the mean is estimated, due to its linear relationship with a bank’s regulatory capital. In addition to using standard information criteria, the degree to which bias reduction in the estimation of the distributional mean can be achieved is used as a measure of model performance. The proposed models outperform the benchmark model with reference to the information criteria and yield a reduction in the distance between the empirical and distributional means. Given the special characteristics of the dataset, where a high proportion of observations are close to zero, a methodology for choosing a rounding threshold in an objective manner is developed as part of the data preparation stage. It is shown how the application of this rounding threshold can reduce bias in moment estimation regardless of the model choice.

Suggested Citation

  • Janette Larney & Gerrit Lodewicus Grobler & James Samuel Allison, 2022. "Introducing Two Parsimonious Standard Power Mixture Models for Bimodal Proportional Data with Application to Loss Given Default," Mathematics, MDPI, vol. 10(23), pages 1-19, November.
  • Handle: RePEc:gam:jmathe:v:10:y:2022:i:23:p:4520-:d:988747
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    References listed on IDEAS

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