IDEAS home Printed from https://ideas.repec.org/a/pab/rmcpee/v16y2013i1p121-142.html
   My bibliography  Save this article

The Compound DGL/Erlang Distribution in the Collective Risk Model || La distribución compuesta DGL/Erlang en el modelo de riesgo colectivo

Author

Listed:
  • Gómez Déniz, Emilio

    (Departamento de Métodos Cuantitativos en Economía y Gestión. Universidad de Las Palmas de Gran Canaria (Spain))

  • Calderín Ojeda, Enrique

    (Centre for Actuarial Studies, Department of Economics. The University of Melbourne (Australia))

Abstract

In this paper the analysis of the collective risk model assuming Erlang loss, when the claim frequency follows the discrete generalized Lindley distribution, is considered. After providing some new results of this discrete model, analytical expressions for the aggregate claim size distribution in general insurance in the case that the discrete generalized Lindley distribution is assumed as the primary distribution while claim size, the secondary distribution, is modeled using an Erlang(r) distribution (r = 1; 2). Comparisons with the compound Poisson and compound negative binomial are developed to explain the viability of the new compound model in two examples in automobile insurance. || En este artículo se analiza el modelo de riesgo colectivo asumiendo que la cantidad individual reclamada sigue una función de densidad Erlang y el número de reclamaciones es una variable aleatoria cuya función masa de probabilidad es la generalizada discreta Lindley. En la primera parte de este trabajo se presentan nuevas propiedades de esta distribución discreta; seguidamente, se calculan expresiones analíticas para la cantidad total reclamada en seguros generales cuando la distribución primaria es la generalizada discreta Lindley, asumiendo la densidad Erlang(r) (r = 1; 2) como distribución secundaria. En la ilustración numérica, el nuevo modelo expuesto en este artículo se compara con los modelos compuestos Poisson y Binomial Negativa en dos ejemplos, en el contexto de seguros de automóviles, para mostrar su efectividad.

Suggested Citation

  • Gómez Déniz, Emilio & Calderín Ojeda, Enrique, 2013. "The Compound DGL/Erlang Distribution in the Collective Risk Model || La distribución compuesta DGL/Erlang en el modelo de riesgo colectivo," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 16(1), pages 121-142, December.
    • Handle: RePEc:pab:rmcpee:v:16:y:2013:i:1:p:121-142
    as

    Download full text from publisher

    File URL: http://www.upo.es/RevMetCuant/pdf/vol16/art81.pdf
    Download Restriction: no
    File URL: http://www.upo.es/RevMetCuant/bibtex.php?id=81
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Dionne, Georges & Vanasse, Charles, 1989. "A Generalization of Automobile Insurance Rating Models: The Negative Binomial Distribution with a Regression Component," ASTIN Bulletin, Cambridge University Press, vol. 19(2), pages 199-212, November.
    2. Agustin Hernandez Bastida & Emilio Gomez Deniz & Jose Maria Perez Sanchez, 2009. "Bayesian robustness of the compound Poisson distribution under bidimensional prior: an application to the collective risk model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 36(8), pages 853-869.
    3. E. Gómez-Déniz, 2010. "Another generalization of the geometric distribution," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(2), pages 399-415, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Angers, Jean-François & Desjardins, Denise & Dionne, Georges & Guertin, François, 2006. "Vehicle and Fleet Random Effects in a Model of Insurance Rating for Fleets of Vehicles," ASTIN Bulletin, Cambridge University Press, vol. 36(1), pages 25-77, May.
    2. García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
    3. Pinquet, Jean, 1998. "Designing Optimal Bonus-Malus Systems from Different Types of Claims," ASTIN Bulletin, Cambridge University Press, vol. 28(2), pages 205-220, November.
    4. Bolancé, Catalina & Guillén, Montserrat & Pinquet, Jean, 2008. "On the link between credibility and frequency premium," Insurance: Mathematics and Economics, Elsevier, vol. 43(2), pages 209-213, October.
    5. Gning, Lucien & Diagne, M.L. & Tchuenche, J.M., 2023. "Hierarchical generalized linear models, correlation and a posteriori ratemaking," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
    6. Jean Pinquet & Georges Dionne & Charles Vanasse & Mathieu Maurice, 2007. "Point-record incentives, asymmetric information and dynamic data," Working Papers hal-00243056, HAL.
    7. Lluís Bermúdez & Dimitris Karlis & Isabel Morillo, 2020. "Modelling Unobserved Heterogeneity in Claim Counts Using Finite Mixture Models," Risks, MDPI, vol. 8(1), pages 1-13, January.
    8. Angers, Jean-François & Desjardins, Denise & Dionne, Georges, 2004. "Modèle Bayésien de tarification de l’assurance des flottes de véhicules," L'Actualité Economique, Société Canadienne de Science Economique, vol. 80(2), pages 253-303, Juin-Sept.
    9. Georges Dionne & Olfa Ghali, 2005. "The (1992) Bonus‐Malus System in Tunisia: An Empirical Evaluation," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 72(4), pages 609-633, December.
    10. Dionne, Georges & Michaud, Pierre-Carl & Pinquet, Jean, 2013. "A review of recent theoretical and empirical analyses of asymmetric information in road safety and automobile insurance," Research in Transportation Economics, Elsevier, vol. 43(1), pages 85-97.
    11. Amela Omeraševiæ & Jasmina Selimoviæ, 2020. "Risk factors selection with data mining methods for insurance premium ratemaking," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics and Business, vol. 38(2), pages 667-696.
    12. Jeong, Himchan & Valdez, Emiliano A., 2020. "Predictive compound risk models with dependence," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 182-195.
    13. Michel Denuit & Yang Lu, 2021. "Wishart‐gamma random effects models with applications to nonlife insurance," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 88(2), pages 443-481, June.
    14. Bermúdez i Morata, Lluís, 2009. "A priori ratemaking using bivariate Poisson regression models," Insurance: Mathematics and Economics, Elsevier, vol. 44(1), pages 135-141, February.
    15. Lluis Bermúdez i Morata, 2008. "A priori ratemaking using bivariate poisson regression models," Working Papers XREAP2008-09, Xarxa de Referència en Economia Aplicada (XREAP), revised Jul 2008.
    16. Jean Pinquet, 2012. "Experience rating in non-life insurance," Working Papers hal-00677100, HAL.
    17. Dionne, Georges, 2012. "The empirical measure of information problems with emphasis on insurance fraud and dynamic data," Working Papers 12-10, HEC Montreal, Canada Research Chair in Risk Management.
    18. Gómez-Déniz, Emilio & Sarabia, José María & Calderín-Ojeda, Enrique, 2011. "A new discrete distribution with actuarial applications," Insurance: Mathematics and Economics, Elsevier, vol. 48(3), pages 406-412, May.
    19. Sarabia, José María & Guillén, Montserrat, 2008. "Joint modelling of the total amount and the number of claims by conditionals," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 466-473, December.
    20. Mihaela DAVID, 2014. "Modeling The Frequency Of Claims In Auto Insurance With Application To A French Case," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 13, pages 69-85, June.

    More about this item

    Keywords

    automobile insurance; collective risk model; Lindley distribution; seguro de automóviles; modelo de riesgo colectivo; distribución Lindley;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • M20 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics - - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pab:rmcpee:v:16:y:2013:i:1:p:121-142. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Publicación Digital - UPO (email available below). General contact details of provider: https://edirc.repec.org/data/dmupoes.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.