On the (weak) dependence between risk proles in insurance data analysis.

• Autores: Francisco José Vázquez Polo , María del Carmen Martel Escobar, Agustín Hernández Bastida
• Localización: Anales de ASEPUMA, ISSN-e 2171-892X, Nº. 21, 2013, 13 págs.
• Idioma: inglés
• Enlaces
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• Resumen

  • A common assumption in the statistical model for Bayes premium in the insurance context, is the independence between risk profiles associated with random quantities considered. In this communication we consider the compound collective risk model in which the primary distribution is comprised of the Poisson-Lindley distribution with a  parameter, and where the secondary distribution is an exponential one with a  parameter. We consider the case of dependence between risk pro les (i.e., the parameters  and ), where the dependence is modelled by a Farlie-Gumbel-Morgenstern family. Statistical properties and some consequences on the Bayes premium of the structure dependence chosen are studied.

• Referencias bibliográficas
  • Berger, J.O. and Moreno, E. (1994). “Bayesian robustness in bidimensional models: prior independence (with discussion)”. Journal of Statistical...
  • Cossette, H.; Marceau, E. and Marri, F. (2008). “On the compound Poisson risk model with dependence based on a generalized Farlie–Gumbel–...
  • D’Este G.M. (1981). “A Morgenstern–type bivariate gamma distribution”. Biometrika, 68, pp. 339–340.
  • De la Horra, J. and Fernandez, C. ´ (1995). “Sensitivity to prior independence via Farlie–Gumbel–Morgenstern model”. Communications in Statistics:...
  • Ghitany, M.E.; Al–Mutairi, D.K. and Nadarajah, S. (2008). “Zero–truncated Poisson–Lindley distribution and its applications”. Mathematics...
  • Ghitany, M.E. and Al–Mutairi, D.K. (2009). “Estimation methods for the discrete Poisson–Lindley distribution”. Journal of Statistical Computation...
  • Hernandez Bastida, A.; Fern ´ andez–S ´ anchez, M.P.; Gómez Deniz, E. ´ (2011). “Collective risk model: Poisson–Lindley and exponential distributions...
  • Lavine, M.; Wasserman, L. and Wolpert, R. (1991). “Bayesian inference with specified prior marginals”. Journal of the American Statistical...
  • Miller, R. and Hickman, J. (1974). “Insurance credibility theory and Bayesian estimation”. In Kahn, P. M. (ed.) Credibility theory and applications,...
  • Morgenstern, D. (1956). “Einfache beispiele zweidimensionaler verteilungen”. Mitt. Math. Statistik, 8, pp. 234–235.
  • Peters, G.W., Shevchenko, P.V. and Wuthrich, M.V. ¨ (2008). “Dynamic operational risk: modelling dependence and combining different sources...
  • Sankaran, M. (1970). “The discrete Poisson–Lindley distribution”. Biometrics, 26, pp. 145–149.
  • Scollnik, D.P.M. (1995). “Bayesian analysis of two overdispersed Poisson regression models”. Communications in Statistics: Theory and Methods,...
  • Sivaganesan, S. (1991). “Sensitivity of some posterior summaries when the prior is unimodal with specified quantiles”. Canadian Journal of...
  • Wasserman, L.; Lavine, M. and Wolpert, R. (1993). “Linearization of Bayesian robustness problems”. Journal of Statistical Planning and Inference,...