BibTex RIS Kaynak Göster

A New Method for Evaulation of Bivariate Compound Poisson Distribution for Aggregate Claims

Yıl 2011, Cilt: 24 Sayı: 2, 241 - 248, 05.04.2011

Öz

In this paper, a bivariate compound Poisson model is proposed for calculating the aggregate claims distribution in a discrete framework and the probabilistic characteristics of this model, such as the joint probability function, joint probability generating function, correlation coefficient and covariance are derived. Then, an algorithm is prepared in Oracle database to obtain the probabilities quickly. By means of prepared algorithm some numerical examples are also given to illustrate the usage of the bivariate compound Poisson model.

 

Key Words: Bivariate compound Poisson distribution, correlation coefficient, joint probability generating function, insurance, claim severity.

Kaynakça

  • Cummins, D.J., Wiltbank, L.J., “Estimating the total claims distribution using multivariate frequency and severity distributions”, Journal of Risk and Insurance, 50: 377–403 (1983).
  • Cossette, H., Gaillardetz, P., Marceau, É., Rioux, J., “On two dependent individual risk models”, Insurance: Mathematics and Economics, 30: 153– 166 (2002).
  • Sundt, B., “On some extensions of Panjer’s class of counting distributions”, Astin Bulletin, 22: 61-80 (1992).
  • Homer, D.L., Clark, D.R., “Insurance applications of bivariate distributions”, CAS Forum, 274-307 (2003).
  • Walhin, J., “On the Optimality of Multiline Excess of Loss Covers”, CAS Forum, 231-243 (2003).
  • Bruno, M.G., Camerini, E., Manna, A., Tomassetti, A., “A new method for evaluating the distribution of aggregate claims”, Applied Mathematics and Computation, 176: 488-505 (2006).
  • Rolski, T., Schmidli, H., Schmidt, V., Teugels, J., “Stochastic Processes for Insurance and Finance”, John Wiley and Sons, (1999).
  • Sundt, B., “On some extensions of Panjer's class of counting distributions”, ASTIN Bulletin, 22: 61-80 (1992).
  • Ozel, G., Inal, C., “The Probability Function of the Compound Poisson Distribution Using Integer Partitions and Ferrer’s Graph”, Bulletin of Statistics and Economics, 2 (1): 75-87 (2008).
  • Ozel, G., Inal, C., “The probability function of the compound Poisson process and an application to aftershock sequences”, Environmetrics, 19: 79-85 (2008).
  • Ozel, G., Inal, C., “The probability function of a geometric Poisson distribution”, Journal of Statistical Computation and Simulation, 80: 479- 487 (2010).
  • Kocherlakota, S., Kocherlakota, K., “Bivariate
  • Discrete Distributions”, Marcel Decker, New York, (1992).
  • Johnson, N.L., Kotz, S., Balakrishnan, N., “Discrete Multivariate Distributions”, Wiley, New York, (1997).
  • Holgate, P., “Estimation for the bivariate Poisson distribution”, Biometrika, 51: 241–245 (1964). [15] Ambagaspitiya, R., “Compound bivariate Lagrangian Poisson distributions”, Insurance: Mathematics & Economics, 23 (1): 21-31 (1998).
  • Homer, D.L., “Aggregating bivariate claim severities with numerical Fourier inversion”, CAS Forum, (2006).
Yıl 2011, Cilt: 24 Sayı: 2, 241 - 248, 05.04.2011

Öz

Kaynakça

  • Cummins, D.J., Wiltbank, L.J., “Estimating the total claims distribution using multivariate frequency and severity distributions”, Journal of Risk and Insurance, 50: 377–403 (1983).
  • Cossette, H., Gaillardetz, P., Marceau, É., Rioux, J., “On two dependent individual risk models”, Insurance: Mathematics and Economics, 30: 153– 166 (2002).
  • Sundt, B., “On some extensions of Panjer’s class of counting distributions”, Astin Bulletin, 22: 61-80 (1992).
  • Homer, D.L., Clark, D.R., “Insurance applications of bivariate distributions”, CAS Forum, 274-307 (2003).
  • Walhin, J., “On the Optimality of Multiline Excess of Loss Covers”, CAS Forum, 231-243 (2003).
  • Bruno, M.G., Camerini, E., Manna, A., Tomassetti, A., “A new method for evaluating the distribution of aggregate claims”, Applied Mathematics and Computation, 176: 488-505 (2006).
  • Rolski, T., Schmidli, H., Schmidt, V., Teugels, J., “Stochastic Processes for Insurance and Finance”, John Wiley and Sons, (1999).
  • Sundt, B., “On some extensions of Panjer's class of counting distributions”, ASTIN Bulletin, 22: 61-80 (1992).
  • Ozel, G., Inal, C., “The Probability Function of the Compound Poisson Distribution Using Integer Partitions and Ferrer’s Graph”, Bulletin of Statistics and Economics, 2 (1): 75-87 (2008).
  • Ozel, G., Inal, C., “The probability function of the compound Poisson process and an application to aftershock sequences”, Environmetrics, 19: 79-85 (2008).
  • Ozel, G., Inal, C., “The probability function of a geometric Poisson distribution”, Journal of Statistical Computation and Simulation, 80: 479- 487 (2010).
  • Kocherlakota, S., Kocherlakota, K., “Bivariate
  • Discrete Distributions”, Marcel Decker, New York, (1992).
  • Johnson, N.L., Kotz, S., Balakrishnan, N., “Discrete Multivariate Distributions”, Wiley, New York, (1997).
  • Holgate, P., “Estimation for the bivariate Poisson distribution”, Biometrika, 51: 241–245 (1964). [15] Ambagaspitiya, R., “Compound bivariate Lagrangian Poisson distributions”, Insurance: Mathematics & Economics, 23 (1): 21-31 (1998).
  • Homer, D.L., “Aggregating bivariate claim severities with numerical Fourier inversion”, CAS Forum, (2006).
Toplam 16 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Statistics
Yazarlar

Gamze Özel

Yayımlanma Tarihi 5 Nisan 2011
Yayımlandığı Sayı Yıl 2011 Cilt: 24 Sayı: 2

Kaynak Göster

APA Özel, G. (2011). A New Method for Evaulation of Bivariate Compound Poisson Distribution for Aggregate Claims. Gazi University Journal of Science, 24(2), 241-248.
AMA Özel G. A New Method for Evaulation of Bivariate Compound Poisson Distribution for Aggregate Claims. Gazi University Journal of Science. Nisan 2011;24(2):241-248.
Chicago Özel, Gamze. “A New Method for Evaulation of Bivariate Compound Poisson Distribution for Aggregate Claims”. Gazi University Journal of Science 24, sy. 2 (Nisan 2011): 241-48.
EndNote Özel G (01 Nisan 2011) A New Method for Evaulation of Bivariate Compound Poisson Distribution for Aggregate Claims. Gazi University Journal of Science 24 2 241–248.
IEEE G. Özel, “A New Method for Evaulation of Bivariate Compound Poisson Distribution for Aggregate Claims”, Gazi University Journal of Science, c. 24, sy. 2, ss. 241–248, 2011.
ISNAD Özel, Gamze. “A New Method for Evaulation of Bivariate Compound Poisson Distribution for Aggregate Claims”. Gazi University Journal of Science 24/2 (Nisan 2011), 241-248.
JAMA Özel G. A New Method for Evaulation of Bivariate Compound Poisson Distribution for Aggregate Claims. Gazi University Journal of Science. 2011;24:241–248.
MLA Özel, Gamze. “A New Method for Evaulation of Bivariate Compound Poisson Distribution for Aggregate Claims”. Gazi University Journal of Science, c. 24, sy. 2, 2011, ss. 241-8.
Vancouver Özel G. A New Method for Evaulation of Bivariate Compound Poisson Distribution for Aggregate Claims. Gazi University Journal of Science. 2011;24(2):241-8.