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ASYMPTOTIC RESULTS FOR AN INVENTORY MODEL OF TYPE s, S WITH A GENERALIZED BETA INTERFERENCE OF CHANCE

Yıl 2011, Cilt: 01 Sayı: 2, 223 - 236, 01.12.2011

Öz

In this study, asymptotic expansion for ergodic distribution of an inventory control model of type s, S with generalized beta interference of chance is obtained, when S − s → ∞. Moreover, weak convergence theorem is proved for ergodic distribution. Finally, the accuracy of the asymptotic expansion is examined with Monte Carlo simulation method.

Kaynakça

  • Aliyev, R., Kucuk, Z. and Khaniyev,T., (2010), Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance, Applied Mathematical Modelling, 34, 3599-3607.
  • Alsmeyer, G., (1991), Some relations between harmonic renewal measure and certain first passage times, Statistics & Probability Letters, 12(1), 19-27.
  • Aras, G. and Woodroofe, M., (1993), Asymptotic expansions for the moments of a randomly stopped average, Annals of Statistics, 21, 503-519.
  • Borovkov, A. A., (1976), Stochastic Processes in Queuing Theory, Springer-Verlag, New York.
  • Brown, M. and Solomon, H. A., (1975), Second-order approximation for the variance of a renewal- reward process, Stochastic Processes and Their Applications, 3, 301-314.
  • Eaton, J.W., (2002), GNU Octave Manual, Network Theory Limited.
  • Feller, W., (1971), Introduction to Probability Theory and Its Applications II, John Wiley.
  • Gihman, I. I. and Skorohod, A. V., (1975), Theory of Stochastic Processes II, Springer, Berlin.
  • Khaniyev, T. and Atalay, K.D., (2010), On the weak convergence of the ergodic distribution for an inventory model of type (s,s), Hacettepe Journal of Mathematics and Statistics, 39(4), 599-611.
  • Khaniyev, T. A., Kesemen, T., Aliyev, R.T. and Kokangl, A., (2008), Asymptotic expansions for the moments of a semi-markovian random walk with exponential distributed inference of chance, Statistics & Probability Letters, 78(6), 785-793.
  • Khaniyev, T. A. and Mammadova, Z., (2006), 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.
  • Korolyuk, V. S. and Borovskikh, Y. V., (1981), Analytical Problems for Asymptotics of Probability Distributions, Naukova, Durnka, Kiev.
  • Pham-Gia, T. and Turkkan, N., (2002), The product and quotient of generalized beta distribution. Statistical Papers, 43, 537-550.
  • Prabhu, N.U., (1981), Stochastic Storage Processes, Springer-Verlag, New York.
Yıl 2011, Cilt: 01 Sayı: 2, 223 - 236, 01.12.2011

Öz

Kaynakça

  • Aliyev, R., Kucuk, Z. and Khaniyev,T., (2010), Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance, Applied Mathematical Modelling, 34, 3599-3607.
  • Alsmeyer, G., (1991), Some relations between harmonic renewal measure and certain first passage times, Statistics & Probability Letters, 12(1), 19-27.
  • Aras, G. and Woodroofe, M., (1993), Asymptotic expansions for the moments of a randomly stopped average, Annals of Statistics, 21, 503-519.
  • Borovkov, A. A., (1976), Stochastic Processes in Queuing Theory, Springer-Verlag, New York.
  • Brown, M. and Solomon, H. A., (1975), Second-order approximation for the variance of a renewal- reward process, Stochastic Processes and Their Applications, 3, 301-314.
  • Eaton, J.W., (2002), GNU Octave Manual, Network Theory Limited.
  • Feller, W., (1971), Introduction to Probability Theory and Its Applications II, John Wiley.
  • Gihman, I. I. and Skorohod, A. V., (1975), Theory of Stochastic Processes II, Springer, Berlin.
  • Khaniyev, T. and Atalay, K.D., (2010), On the weak convergence of the ergodic distribution for an inventory model of type (s,s), Hacettepe Journal of Mathematics and Statistics, 39(4), 599-611.
  • Khaniyev, T. A., Kesemen, T., Aliyev, R.T. and Kokangl, A., (2008), Asymptotic expansions for the moments of a semi-markovian random walk with exponential distributed inference of chance, Statistics & Probability Letters, 78(6), 785-793.
  • Khaniyev, T. A. and Mammadova, Z., (2006), 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.
  • Korolyuk, V. S. and Borovskikh, Y. V., (1981), Analytical Problems for Asymptotics of Probability Distributions, Naukova, Durnka, Kiev.
  • Pham-Gia, T. and Turkkan, N., (2002), The product and quotient of generalized beta distribution. Statistical Papers, 43, 537-550.
  • Prabhu, N.U., (1981), Stochastic Storage Processes, Springer-Verlag, New York.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Tahir Khaniyev Bu kişi benim

Cihan Aksop Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2011
Yayımlandığı Sayı Yıl 2011 Cilt: 01 Sayı: 2

Kaynak Göster