Abstract
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.
Keywords
Bivariate compound Poisson distribution correlation coefficient joint probability generating function insurance claim severity.
References
- 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).
Abstract
References
- 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).
Details
| Primary Language | English |
|---|---|
| Journal Section | Statistics |
| Authors | |
| Publication Date | April 5, 2011 |
| Published in Issue | Year 2011 Volume: 24 Issue: 2 |