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Modelling of Loan Non-Payments with Count Distributions Arising from Non-Exponential Inter-Arrival Times

Author

Listed:
  • Yeh-Ching Low

    (Department of Computing and Information Systems, Sunway University, Petaling Jaya 47500, Malaysia)

  • Seng-Huat Ong

    (Institute of Actuarial Science and Data Analytics, UCSI University, Kuala Lumpur 56000, Malaysia
    Institute of Mathematical Sciences, University of Malaya, Kuala Lumpur 50603, Malaysia)

Abstract

The number of non-payments is an indicator of delinquent behaviour in credit scoring, hence its estimation and prediction are of interest. The modelling of the number of non-payments, as count data, can be examined as a renewal process. In a renewal process, the number of events (such as non-payments) which has occurred up to a fixed time t is intimately connected with the inter-arrival times between the events. In the context of non-payments, the inter-arrival times correspond to the time between two subsequent non-payments. The probability mass function and the renewal function of the count distribution are often complicated, with terms involving factorial and gamma functions, and thus their computation may encounter numerical difficulties. In this paper, with the motivation of modelling the number of non-payments through a renewal process, a general method for computing the probabilities and the renewal function based on numerical Laplace transform inversion is discussed. This method is applied to some count distributions which are derived given the distributions of the inter-arrival times. Parameter estimation with maximum likelihood estimation is considered, with an application to a data set on number of non-payments from the literature.

Suggested Citation

  • Yeh-Ching Low & Seng-Huat Ong, 2023. "Modelling of Loan Non-Payments with Count Distributions Arising from Non-Exponential Inter-Arrival Times," JRFM, MDPI, vol. 16(3), pages 1-14, February.
    • Handle: RePEc:gam:jjrfmx:v:16:y:2023:i:3:p:150-:d:1078390
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    References listed on IDEAS

    as
    1. Kanichukattu K. Jose & Bindu Abraham, 2011. "A count model based on Mittag-Leffler interarrival times," Statistica, Department of Statistics, University of Bologna, vol. 71(4), pages 501-514.
    2. Anna, Petrenko, . "Мaркування готової продукції як складова частина інформаційного забезпечення маркетингової діяльності підприємств овочепродуктового підкомплексу," Agricultural and Resource Economics: International Scientific E-Journal, Agricultural and Resource Economics: International Scientific E-Journal, vol. 2(01).
    3. repec:bot:journl:v:71:y:2011:i:4:p:501-514 is not listed on IDEAS
    4. Sami Mestiri & Abdeljelil Farhat, 2021. "Using Non-parametric Count Model for Credit Scoring," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(1), pages 39-49, March.
    5. Matuszyk, Anna & So, Mee Chi & Mues, Christophe & Moore, Angela, 2016. "Modelling repayment patterns in the collections process for unsecured consumer debt: A case studyAuthor-Name: Thomas, Lyn C," European Journal of Operational Research, Elsevier, vol. 249(2), pages 476-486.
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