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A Sarmanov Distribution with Beta Marginals: An Application to Motor Insurance Pricing

Author

Listed:
  • Catalina Bolancé

    (Department Econometrics, Riskcenter-IREA, Universitat de Barcelona, E08034 Barcelona, Spain
    These authors contributed equally to this work.)

  • Montserrat Guillen

    (Department Econometrics, Riskcenter-IREA, Universitat de Barcelona, E08034 Barcelona, Spain
    These authors contributed equally to this work.)

  • Albert Pitarque

    (Department Econometrics, Riskcenter-IREA, Universitat de Barcelona, E08034 Barcelona, Spain
    These authors contributed equally to this work.)

Abstract

Background: The Beta distribution is useful for fitting variables that measure a probability or a relative frequency. Methods: We propose a Sarmanov distribution with Beta marginals specified as generalised linear models. We analyse its theoretical properties and its dependence limits. Results: We use a real motor insurance sample of drivers and analyse the percentage of kilometres driven above the posted speed limit and the percentage of kilometres driven at night, together with some additional covariates. We fit a Beta model for the marginals of the bivariate Sarmanov distribution. Conclusions: We find negative dependence in the high quantiles indicating that excess speed and night-time driving are not uniformly correlated.

Suggested Citation

  • Catalina Bolancé & Montserrat Guillen & Albert Pitarque, 2020. "A Sarmanov Distribution with Beta Marginals: An Application to Motor Insurance Pricing," Mathematics, MDPI, vol. 8(11), pages 1-11, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:2020-:d:444234
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    References listed on IDEAS

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    1. Ana M. Pérez-Marín & Montserrat Guillen & Manuela Alcañiz & Lluís Bermúdez, 2019. "Quantile Regression with Telematics Information to Assess the Risk of Driving above the Posted Speed Limit," Risks, MDPI, vol. 7(3), pages 1-11, July.
    2. Silvia Ferrari & Francisco Cribari-Neto, 2004. "Beta Regression for Modelling Rates and Proportions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 31(7), pages 799-815.
    3. Arnold, Barry C. & Tony Ng, Hon Keung, 2011. "Flexible bivariate beta distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(8), pages 1194-1202, September.
    4. Olkin, Ingram & Liu, Ruixue, 2003. "A bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 62(4), pages 407-412, May.
    5. Bolancé, Catalina & Vernic, Raluca, 2019. "Multivariate count data generalized linear models: Three approaches based on the Sarmanov distribution," Insurance: Mathematics and Economics, Elsevier, vol. 85(C), pages 89-103.
    6. Olkin, Ingram & Trikalinos, Thomas A., 2015. "Constructions for a bivariate beta distribution," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 54-60.
    7. A. Gupta & C. Wong, 1985. "On three and five parameter bivariate beta distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 85-91, December.
    8. Mercedes Ayuso & Montserrat Guillen & Jens Perch Nielsen, 2019. "Improving automobile insurance ratemaking using telematics: incorporating mileage and driver behaviour data," Transportation, Springer, vol. 46(3), pages 735-752, June.
    9. Montserrat Guillen & Jens Perch Nielsen & Mercedes Ayuso & Ana M. Pérez‐Marín, 2019. "The Use of Telematics Devices to Improve Automobile Insurance Rates," Risk Analysis, John Wiley & Sons, vol. 39(3), pages 662-672, March.
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    Cited by:

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    2. Anas Abdallah & Lan Wang, 2023. "Rank-Based Multivariate Sarmanov for Modeling Dependence between Loss Reserves," Risks, MDPI, vol. 11(11), pages 1-37, October.
    3. Tzougas, George & Makariou, Despoina, 2022. "The multivariate Poisson-Generalized Inverse Gaussian claim count regression model with varying dispersion and shape parameters," LSE Research Online Documents on Economics 117197, London School of Economics and Political Science, LSE Library.

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