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

Year 2011, Volume 01, Issue 2, 223 - 236, 01.12.2011

Abstract

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.

References

  • 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.

Year 2011, Volume 01, Issue 2, 223 - 236, 01.12.2011

Abstract

References

  • 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.

Details

Primary Language English
Journal Section Research Article
Authors

Tahir KHANİYEV This is me
TOBB University of Economics and Technology, Department of Industrial Engineering, Ankara, Turkey and Azerbaijan National Academy of Sciences, Institute of Cybernetics, Baku, Azerbaijan


Cihan AKSOP This is me
The Scientific and Technological Research Council of Turkey, Science and Society Department, Ankara, Turkey and Gazi University, Department of Statistics, Ankara, Turkey

Publication Date December 1, 2011
Published in Issue Year 2011, Volume 01, Issue 2

Cite

Bibtex @ { twmsjaem761800, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2011}, volume = {01}, number = {2}, pages = {223 - 236}, title = {ASYMPTOTIC RESULTS FOR AN INVENTORY MODEL OF TYPE s, S WITH A GENERALIZED BETA INTERFERENCE OF CHANCE}, key = {cite}, author = {Khaniyev, Tahir and Aksop, Cihan} }