ASYMPTOTIC RESULTS FOR AN INVENTORY MODEL OF TYPE s, S WITH A GENERALIZED BETA INTERFERENCE OF CHANCE
ASYMPTOTIC RESULTS FOR AN INVENTORY MODEL OF TYPE s, S WITH A GENERALIZED BETA INTERFERENCE OF CHANCE
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.
Keywords:
Inventory model of type s, S, renewal-reward process, generalized betadistribution, asymptotic expansion weak convergence, Monte Carlo simulation,
___
- 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.
- ISSN: 2146-1147
- Başlangıç: 2010
- Yayıncı: Turkic World Mathematical Society