BibTex RIS Kaynak Göster

ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL

Yıl 2016, Cilt: 29 Sayı: 3, 615 - 626, 30.09.2016

Öz

In this study, a semi-Markovian random walk (X(t)) with Pareto distributed interference of chance and delay is considered. Some exact formulas for the first four stationary moments of the process X(t) are obtained, when the random variables $\zetta_n,n=1,2,...$ which express the discrete interference of chance have Pareto distribution with parameters $(\alpha, \lamda)$. The random variables $\zetta_n,n=1,2,...$ are interpreted as loans which insurance company gets from a bank. With the use of these exact formulas, the third-order asymptotic expansions for the first four stationary moments of the process X(t) are derived, when $E(zetta_n)$ is sufficiently large. Finally, by using Monte-Carlo simulation method, the accuracy of obtained approximation formulas is tested.

Kaynakça

  • Aliyev, R.T., Khaniyev, T.A. and Kesemen, T., “Asymptotic expansions for the moments of a semi-Markovian random walk with gamma distributed interference of chance”, Communications in Statistics- Theory and Methods, 39(1): 130-143, (2010).
  • Aliyev, R., Kucuk, Z. and Khaniyev, T., “Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance”, Applied Mathematical Modelling, 34(11):3599-3607, (2010).
  • Anisimov, V.V. and Artalejo, J.R., “Analysis of Markov multiserver retrial queues with negative arrivals”, Queuing Systems: Theory and Applic., 39(2/3):157–182, (2001).
  • Borovkov, A.A., Stochastic Process in Queuing Theory, Springer, New York, (1976).
  • Feller, W., Introduction to Probability Theory and Its Appl. II, New York, (1971)
  • Gihman, I.I. and Skorohod, A.V., Theory of Stochastic Processes II, Berlin, (1975).
  • Khaniyev, T.A. and Mammadova, Z. “On the stationary characteristics of the extended model of type (s,S) with Gaussian distribution of summands”, Journal of Statistical Computation and Simulation, 76(10): 861–874 , (2006).
  • Khaniyev, T.A., Kesemen, T., Aliyev, R.T. and Kokangul, A., “Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance”, Statistics & Probability Letters, 78(6):785–793, (2008).
  • Lotov, V.I., “On some boundary crossing problems for Gaussian random walks”, The Annals of Probability, 24(4): 2154–2171, (1996).
  • Rogozin, B.A., “On the distribution of the first jump”, Theory Probability and Its Applications, 9(3):498–545, (1964).
Yıl 2016, Cilt: 29 Sayı: 3, 615 - 626, 30.09.2016

Öz

Kaynakça

  • Aliyev, R.T., Khaniyev, T.A. and Kesemen, T., “Asymptotic expansions for the moments of a semi-Markovian random walk with gamma distributed interference of chance”, Communications in Statistics- Theory and Methods, 39(1): 130-143, (2010).
  • Aliyev, R., Kucuk, Z. and Khaniyev, T., “Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance”, Applied Mathematical Modelling, 34(11):3599-3607, (2010).
  • Anisimov, V.V. and Artalejo, J.R., “Analysis of Markov multiserver retrial queues with negative arrivals”, Queuing Systems: Theory and Applic., 39(2/3):157–182, (2001).
  • Borovkov, A.A., Stochastic Process in Queuing Theory, Springer, New York, (1976).
  • Feller, W., Introduction to Probability Theory and Its Appl. II, New York, (1971)
  • Gihman, I.I. and Skorohod, A.V., Theory of Stochastic Processes II, Berlin, (1975).
  • Khaniyev, T.A. and Mammadova, Z. “On the stationary characteristics of the extended model of type (s,S) with Gaussian distribution of summands”, Journal of Statistical Computation and Simulation, 76(10): 861–874 , (2006).
  • Khaniyev, T.A., Kesemen, T., Aliyev, R.T. and Kokangul, A., “Asymptotic expansions for the moments of a semi-Markovian random walk with exponential distributed interference of chance”, Statistics & Probability Letters, 78(6):785–793, (2008).
  • Lotov, V.I., “On some boundary crossing problems for Gaussian random walks”, The Annals of Probability, 24(4): 2154–2171, (1996).
  • Rogozin, B.A., “On the distribution of the first jump”, Theory Probability and Its Applications, 9(3):498–545, (1964).
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Bölüm Statistics
Yazarlar

Zafer Küçük Bu kişi benim

Tülay Kesemen

Tahir Khaniyev

Fuat Yetim Bu kişi benim

Aslı Bektaş Kamışlık Bu kişi benim

Yayımlanma Tarihi 30 Eylül 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 29 Sayı: 3

Kaynak Göster

APA Küçük, Z., Kesemen, T., Khaniyev, T., Yetim, F., vd. (2016). ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL. Gazi University Journal of Science, 29(3), 615-626.
AMA Küçük Z, Kesemen T, Khaniyev T, Yetim F, Bektaş Kamışlık A. ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL. Gazi University Journal of Science. Eylül 2016;29(3):615-626.
Chicago Küçük, Zafer, Tülay Kesemen, Tahir Khaniyev, Fuat Yetim, ve Aslı Bektaş Kamışlık. “ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL”. Gazi University Journal of Science 29, sy. 3 (Eylül 2016): 615-26.
EndNote Küçük Z, Kesemen T, Khaniyev T, Yetim F, Bektaş Kamışlık A (01 Eylül 2016) ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL. Gazi University Journal of Science 29 3 615–626.
IEEE Z. Küçük, T. Kesemen, T. Khaniyev, F. Yetim, ve A. Bektaş Kamışlık, “ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL”, Gazi University Journal of Science, c. 29, sy. 3, ss. 615–626, 2016.
ISNAD Küçük, Zafer vd. “ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL”. Gazi University Journal of Science 29/3 (Eylül 2016), 615-626.
JAMA Küçük Z, Kesemen T, Khaniyev T, Yetim F, Bektaş Kamışlık A. ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL. Gazi University Journal of Science. 2016;29:615–626.
MLA Küçük, Zafer vd. “ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL”. Gazi University Journal of Science, c. 29, sy. 3, 2016, ss. 615-26.
Vancouver Küçük Z, Kesemen T, Khaniyev T, Yetim F, Bektaş Kamışlık A. ON APPLICATION OF RANDOM WALK WITH DELAY AND PARETO DISTRIBUTED INTERFERENCE OF CHANCE TO AN INSURANCE MODEL. Gazi University Journal of Science. 2016;29(3):615-26.