On Approximation of the Panjer Distribution by the Poisson and Binomial Distributions-Reference-Cited by-同舟云学术

On Approximation of the Panjer Distribution by the Poisson and Binomial Distributions

Published:2021-09-30 Issue: Volume:20 Page:520-523
ISSN:2224-2880
Container-title:WSEAS TRANSACTIONS ON MATHEMATICS
language:en
Short-container-title:

Author:

Sahatsathatsana Chanokgan¹,Sahatsathatsana Sattra²

Affiliation:

1. Department of Science and Mathematics Faculty of Science and Health Technology Kalasin University, 46000, THAILAND

2. Department of Foreign Language Faculty of Liberal Arts Kalasin University, 46000, THAILAND

Abstract

The aim of this paper is to approximate the panjer distribution by the poisson and binomial distributions, where each bound is obtained by using the z-function and the Stein-Chen identity. For these bounds, it is indicated that a result of each of the Poisson and Binomial approximations yields a good approximation if both α and λ are small.

Publisher

World Scientific and Engineering Academy and Society (WSEAS)

Subject

General Mathematics

Reference13 articles.

1. A. D. Barbour, L. Holst and S. Janson, Poisson approximation, The Clarendon Press Oxford University Press, 1992, 2.

2. B. Sundt and W. S. Jewell, Further results on recursive evaluation of compound distributions, ASTIN Bulletin: The Journal of the IAA, 12(1), 1981, pp. 27–39.

3. C. Stein, A bound for the error in the normal approximation to the distribution of a sum of dependent random variables, In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Volume 2: Probability Theory The Regents of the University of California, 1972.

4. G. Peters, A.M. hansen. & A. Doucet, Simulation of the Annual Loss Distribution in Operational Risk via Panjer Recursions and Volterra Integral Equations for Value at Risk and Expected Shortfall Estimation, Available at SSRN 2980408, 2017

5. I. Schlangen, E.D. Delande, J. Houssineau and D.E. Clark, A second-order PHD filter with mean and variance in target number, IEEE Transactions on Signal Processing, 66(1), 2017, pp. 48- 63.