Abstract
References
- Aki, S., Kuboku, H. and Hirano, K. (1984). On discrete distributions of order k. Annals of the Institute of Statistical Mathematics, 36, Part A, 431-440.
- Balakrishnan, N. and Koutras, M.V. (2002). Runs and Scans with Applications. Wiley Series in Probability and Statistics.
- Charalambides, Ch. (1986). On discrete distributions of order k. Annals of the Institute of Statistical Mathematics, 38, Part A, 557-568.
- Chukova, S. and Minkova, L.D. (2015). P´olya-Aeppli of order k risk model. Communications in Statistics - Simulation and Computation, 44, 551-564.
- Chukova, S. and Minkova, L.D. (2013). Characterization of the P´olya-Aeppli process. Stochastic Analysis and Applications, 31, 590-599.
- Dufresne, F. and Gerber, H.U. (1989). Three methods to calculate the probability of ruin. Astin Bulletin., 19(1), 71-90.
- Gerber, H.U. and Shiu, E.S.W. (1998). On the time value of ruin. North American Actuarial Journal, 2, 48-72.
- Hirano, K. (1986). Some properties of the distributions of order k. in Fibonacci Numbers and Their Applications, A. N. Philippou et al.(eds), 43-53.
- Minkova, L.D. (2004). The P´olya-Aeppli process and ruin problems. Journal of Applied Mathematics and Stochastic Analysis, 3, 221-234.
- Minkova, L.D. (2010). P´olya-Aeppli distribution of order k. Communications in Statistics - Theory and Methods, 39, 408-415.
- Panjer, H. (1981). Recursive evaluation of a family of compound discrete distributions. Astin Bulletin, 12, 22-26.
Abstract
In this paper we propose and study the so called Polya-Aeppli process of order k of the second type. Firstly, the process is defined using probability generating function, followed by its definition as a birth process. The distribution of the related counting process is presented by recursion formulae. The Polya-Aeppli process of order k of the second type is considered within the framework of the risk process and corresponding probability of ruin is studied. Using simulation, some interesting results for the probability of ruin are obtained. Also, a comparison between the Polya-Aeppli process of order k and Polya-Aeppli process of order k of the second type is discussed.
Keywords
P´olya-Aeppli distribution Distributions of order k Compound distributions Ruin probability
References
- Aki, S., Kuboku, H. and Hirano, K. (1984). On discrete distributions of order k. Annals of the Institute of Statistical Mathematics, 36, Part A, 431-440.
- Balakrishnan, N. and Koutras, M.V. (2002). Runs and Scans with Applications. Wiley Series in Probability and Statistics.
- Charalambides, Ch. (1986). On discrete distributions of order k. Annals of the Institute of Statistical Mathematics, 38, Part A, 557-568.
- Chukova, S. and Minkova, L.D. (2015). P´olya-Aeppli of order k risk model. Communications in Statistics - Simulation and Computation, 44, 551-564.
- Chukova, S. and Minkova, L.D. (2013). Characterization of the P´olya-Aeppli process. Stochastic Analysis and Applications, 31, 590-599.
- Dufresne, F. and Gerber, H.U. (1989). Three methods to calculate the probability of ruin. Astin Bulletin., 19(1), 71-90.
- Gerber, H.U. and Shiu, E.S.W. (1998). On the time value of ruin. North American Actuarial Journal, 2, 48-72.
- Hirano, K. (1986). Some properties of the distributions of order k. in Fibonacci Numbers and Their Applications, A. N. Philippou et al.(eds), 43-53.
- Minkova, L.D. (2004). The P´olya-Aeppli process and ruin problems. Journal of Applied Mathematics and Stochastic Analysis, 3, 221-234.
- Minkova, L.D. (2010). P´olya-Aeppli distribution of order k. Communications in Statistics - Theory and Methods, 39, 408-415.
- Panjer, H. (1981). Recursive evaluation of a family of compound discrete distributions. Astin Bulletin, 12, 22-26.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Conference Paper |
| Authors | |
| Acceptance Date | June 23, 2021 |
| Publication Date | December 31, 2021 |
| IZ | https://izlik.org/JA22YL34ES |
| Published in Issue | Year 2021 Volume: 13 Issue: 3 |