Research and Innovation Articles
A relation between the Hofmann’s distribution and Panjer’s distribution
Published 2013-07-29
Keywords
- Panjer’s distribution,
- Hofmann’s distribution,
- Poisson-Pascal dis-tribution,
- Pochhammer’s symbol
How to Cite
Jiménez Moscoso, J. A. (2013). A relation between the Hofmann’s distribution and Panjer’s distribution. Revista Integración, Temas De matemáticas, 31(1), 59–67. Retrieved from https://revistas.uis.edu.co/index.php/revistaintegracion/article/view/3384
Abstract
One of the main objectives of actuarial risk theory is to modelthe number of claims by a classical probability distribution, but due to poor statistical fit obtained sometimes, in actuarial literature it is proposed to usethe Panjer’s family of distributions, since for specific values of its parameters can generate some discrete distributions. This paper shows that the Panjer’s distribution is a particular case of the Hofmann’s distribution.
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References
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[2] Evans D.A., “Experimental evidence concerning contagious distributions in ecology”, Biometrika 40 (1953), 186–211.
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[6] Katti S.K. and Gurland J., “The poisson pascal distribution”, Biometrics 17 (1961), no. 4, 527–538.
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[10] Schmidt K.D. and Zocher M., “Loss reserving and Hofmann distributions”, Schweiz. Aktuarver. Mitt. 2 (2005), no. 2, 127–162.
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[12] Sundt B., “On multivariate Panjer’s recursions”, Astin Bull. 29 (1999), 29–46.
[13] Sundt B. and Jewell W.S., “Further results on recursive evaluation of compound distributions”, Astin Bull. 12 (1981), no. 1, 27–39.
[14] Walhin J.F., “Recursions for actuaries and applications in the field of reinsurance and bonusmalus systems”, Thesis (Ph.D.), Université catholique de Louvain, Institut de statistique, Louvain-la-Neuve, 2000.
[15] Walhin J.F. and Paris J., “Processus de Poisson melange et formules unifiees pour systemes bonus-malus”, Bull. français d’actuariat 3 (1999), no. 6, 35–43.
[2] Evans D.A., “Experimental evidence concerning contagious distributions in ecology”, Biometrika 40 (1953), 186–211.
[3] Fisher R.A., “The negative binomial distribution”, Ann. Eugenics 11 (1941), 182–187.
[4] Grandell J., Mixed Poisson Processes, CRC Monographs on Statistics & Applied Probability, Chapman and Hall, 1997.
[5] Hofmann M., “Über zusammengesetzte Poisson-Prozesse und ihre Anwendungen in der Unfallversicherung”, Mitt. Verein. Schweiz. Versich.-Math. 55 (1955), 499–575.
[6] Katti S.K. and Gurland J., “The poisson pascal distribution”, Biometrics 17 (1961), no. 4, 527–538.
[7] Katz L., “Unified treatment of a broad class of discrete probability distributions”, in Classical and Contagious Discrete Distributions Vol. I, (ed. Patil, G.) Stat. Publishing Soc., (1965) 175–182.
[8] Panjer H.H., “Recursive evaluation of a family of compound distributions”, Astin Bull. 12 (1981), no. 1, 22–26.
[9] Panjer H.H., “Models of claim frequency”, Actuar. Sci. 39 (1986), 115–125.
[10] Schmidt K.D. and Zocher M., “Loss reserving and Hofmann distributions”, Schweiz. Aktuarver. Mitt. 2 (2005), no. 2, 127–162.
[11] Sundt B., “On some extensions of Panjer’s class of counting distributions’, Astin Bull. 22 (1992), 61–80.
[12] Sundt B., “On multivariate Panjer’s recursions”, Astin Bull. 29 (1999), 29–46.
[13] Sundt B. and Jewell W.S., “Further results on recursive evaluation of compound distributions”, Astin Bull. 12 (1981), no. 1, 27–39.
[14] Walhin J.F., “Recursions for actuaries and applications in the field of reinsurance and bonusmalus systems”, Thesis (Ph.D.), Université catholique de Louvain, Institut de statistique, Louvain-la-Neuve, 2000.
[15] Walhin J.F. and Paris J., “Processus de Poisson melange et formules unifiees pour systemes bonus-malus”, Bull. français d’actuariat 3 (1999), no. 6, 35–43.