Öz
In this paper we propose and study a new distribution, called the hypogeometric distribution, which is a sum of independent geometrically distributed variables with different parameters. Also, we propose and study a discrete time point process based on this distribution. As an example, we focus on a particular form of this process. Also, we show that this type of processes could be used as an appropriate tool to model arrivals with increasing or decreasing time trends. Some possible extensions of this work are also included in the paper.
Anahtar Kelimeler
geometric distribution hypogeometric distribution waiting time counting process
Kaynakça
- Belzunce, F., Ortega E-M. and Ruiz, J.M. (2009). Aging properties of a discrete-time failure and repair model. IEEE Transactions on Reliability, 58, 161-171.
- Cossette, H., Landriault, D. and Marceau, Ề. (2004). Exact expressions and upper bound for ruin probabilities in the compound Markov binomial model. Insurance: Mathematics and Economics, 34, 449-466.
- Dickson, D.C.M., Egidio dos Reis, A. and Waters, H.R. (1995). Some stable algorithms in ruin theory and their applications. ASTIN Bulletin, 25, 153-175.
- Kobayashi, H., Mark, B.I. and Turin, W. (2012). Probability, Random Processes, and Statistical Analysis. Cambridge University Press, New York.
- Li, Sh. and Sendova, K.P. (2013). The finite-time ruin probability under the compound binomial risk model. European Actuarial Journal, 3, 249-271.
- Ortega, E-M., Alonso, J. and Ortega-Quiles, E. (2016). Comparison of multistate models with discrete-time pure-birth process for recurrent events and uncertain parameters. Communications in Statistics-Theory and Methods, 45, 1733-1746.
- Ross, S.M. (2007). Introduction to Probability Models. Ninth edition, Elsevier Inc., USA.
- Shaked, M. and Shanthikumar, J.G. (1994). Stochastic Orders and Their Applications. Academic Press, New York.
Öz
Kaynakça
- Belzunce, F., Ortega E-M. and Ruiz, J.M. (2009). Aging properties of a discrete-time failure and repair model. IEEE Transactions on Reliability, 58, 161-171.
- Cossette, H., Landriault, D. and Marceau, Ề. (2004). Exact expressions and upper bound for ruin probabilities in the compound Markov binomial model. Insurance: Mathematics and Economics, 34, 449-466.
- Dickson, D.C.M., Egidio dos Reis, A. and Waters, H.R. (1995). Some stable algorithms in ruin theory and their applications. ASTIN Bulletin, 25, 153-175.
- Kobayashi, H., Mark, B.I. and Turin, W. (2012). Probability, Random Processes, and Statistical Analysis. Cambridge University Press, New York.
- Li, Sh. and Sendova, K.P. (2013). The finite-time ruin probability under the compound binomial risk model. European Actuarial Journal, 3, 249-271.
- Ortega, E-M., Alonso, J. and Ortega-Quiles, E. (2016). Comparison of multistate models with discrete-time pure-birth process for recurrent events and uncertain parameters. Communications in Statistics-Theory and Methods, 45, 1733-1746.
- Ross, S.M. (2007). Introduction to Probability Models. Ninth edition, Elsevier Inc., USA.
- Shaked, M. and Shanthikumar, J.G. (1994). Stochastic Orders and Their Applications. Academic Press, New York.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Matematik |
| Bölüm | Araştırma Makalesi |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Temmuz 2022 |
| Kabul Tarihi | 21 Şubat 2022 |
| Yayımlandığı Sayı | Yıl 2022 Cilt: 14 Sayı: 1 |
