BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 8 Sayı: 1.1, 318 - 329, 01.09.2018

Öz

Kaynakça

  • Aliyev, R. T., (2016), On a stochastic process with a heavy tailed distributed component de- scribing inventory model of type (s,S), Communications in Statistics-Theory and Methods, DOI: 1080/03610926.2014.1002932.
  • Aliyev, R. T., Khaniyev, T., (2014), On the semi-Markovian random walk with Gaussian distribution of summands, Communication in Statistics -Theory and Methods, 43 (1), pp. 90-104.
  • Aliyev, R. T., Khaniyev, T. A., Kesemen, T. (2010), 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), pp. 130-143. Asmussen, S., (2000), Ruin Probabilities, World Scientific Publishing, Singapore.
  • Bingham, N. H., Goldie, C. M., Teugels, J. L., (1987), Regular Variation, Cambridge University Press, Cambridge.
  • Borokov, A. A., Borokov, K. A., (2008), Asymptotic Analysis of Random Walks, Heavy Tailed Dis- tributions, Cambridge University Press, New York.
  • Brown, M., Solomon, H. A., (1975), Second order approximation for the variance of a renewal reward process and their applications, Stochastic Processes and their Applications, 3, 301-314.
  • Chevalier, Judith, Austan, G., (2003), Measuring prices and price competition online: Amazon.com and barnesandnoble.com., Quantitative Marketing and Economics, 1 (2), pp. 203-222.
  • Chen, F., Zheng, Y. S., (1997), Sensitivity analysis of an inventory model of type (s,S) inventory model, Operation Research and Letters, 21, pp. 19-23.
  • Embrechts, P., Kluppelberg, C., Mikosh, T., (1997), Modelling Extremal Events, Springer Verlag.
  • Feller, W., (1971), Introduction to Probability Theory and Its Applications II, John Wiley, New York.
  • Foss, S., Korshunov, D., Zachary, S., (2011), An Introduction to Heavy Tailed and Subexponential
  • Distributions, Springer Series in Operaions Research and Financial Engineering, New York. Gaffeo, Edoardo, Antonello, E. S., Laura, V., (2008), Demand distribution dynamics in creative industries: The market for books in Italy, Information Economics and Policy, 20 (3), pp. 257-268.
  • Geluk, J. L., (1997), A renewal theorem in the finite-mean case, Proceedings of the American Math- ematical Society, 125 (11), pp. 3407-3413.
  • Gikhman, I. I., Skorohod, A. V., (1975), Theory of Stochastic Processes II, Springer: Berlin.
  • Khaniyev, T., Aksop, C., (2011), Asymptotic results for an inventory model of type (s,S) with gener- alized beta interference of chance, TWMS J.App.Eng.Math., 2, pp. 223-236.
  • Khaniyev, T., 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), pp. 599-611.
  • Khaniyev, T., Kokangul, A., Aliyev, R. (2013), An asymptotic approach for a semi Markovian inven- tory model of type (s,S), Applied Stochastic Models in Business and Industry, 29 (5), pp. 439-453.
  • Levy, J., Taqqu, M. S, (1987), On renewal processes having stable inter-renewal intervals and stable rewards, Ann.Sci.Math., 11, pp. 95-110.
  • Resnick, S. I., (2006), Heavy-Tail Phenomena: Probabilistic and Statistical Madeling, Springer Series in Operations Research and Financial Engineering, New York.
  • Seneta, E., (1976), Regularly Varying Functions, Springer-Verlag, New York.
  • Sgibnev, M. S., (2009), On a renewal function when second moment is infinite, Statistics and Proba- bility Letters, 79, pp. 1242-1245.
  • Smith, W. L., (1959), On the cumulants of renewal process, Biometrika 46 (1), pp. 1-29.
  • Teugels, J. L., (1968), Renewal theorems when the second moment is infinite, The Annals of Mathe- matical Statistics 39 (4), pp. 1210-1219.

ON THE MOMENTS FOR ERGODIC DISTRIBUTION OF AN INVENTORY MODEL OF TYPE s; S WITH REGULARLY VARYING DEMANDS HAVING INFINITE VARIANCE

Yıl 2018, Cilt: 8 Sayı: 1.1, 318 - 329, 01.09.2018

Öz

In this study a stochastic process X t which represents a semi Markovian inventory model of type s,S has been considered in the presence of regularly varying tailed demand quantities. The main purpose of the current study is to investigate the asymptotic behavior of the moments of ergodic distribution of the process X t when the demands have any arbitrary distribution function from the regularly varying subclass of heavy tailed distributions with in nite variance. In order to obtain renewal function generated by the regularly varying random variables, we used a special asymptotic expansion provided by Geluk [14]. As a rst step we investigate the current problem with the whole class of regularly varying distributions with tail parameter 1 < < 2 rather than a single distribution. We obtained a general formula for the asymptotic expressions of nth order moments n = 1; 2; 3; : : : of ergodic distribution of the process X t . Subsequently we consider this system with Pareto distributed demand random variables and apply obtained results in this special case.

Kaynakça

  • Aliyev, R. T., (2016), On a stochastic process with a heavy tailed distributed component de- scribing inventory model of type (s,S), Communications in Statistics-Theory and Methods, DOI: 1080/03610926.2014.1002932.
  • Aliyev, R. T., Khaniyev, T., (2014), On the semi-Markovian random walk with Gaussian distribution of summands, Communication in Statistics -Theory and Methods, 43 (1), pp. 90-104.
  • Aliyev, R. T., Khaniyev, T. A., Kesemen, T. (2010), 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), pp. 130-143. Asmussen, S., (2000), Ruin Probabilities, World Scientific Publishing, Singapore.
  • Bingham, N. H., Goldie, C. M., Teugels, J. L., (1987), Regular Variation, Cambridge University Press, Cambridge.
  • Borokov, A. A., Borokov, K. A., (2008), Asymptotic Analysis of Random Walks, Heavy Tailed Dis- tributions, Cambridge University Press, New York.
  • Brown, M., Solomon, H. A., (1975), Second order approximation for the variance of a renewal reward process and their applications, Stochastic Processes and their Applications, 3, 301-314.
  • Chevalier, Judith, Austan, G., (2003), Measuring prices and price competition online: Amazon.com and barnesandnoble.com., Quantitative Marketing and Economics, 1 (2), pp. 203-222.
  • Chen, F., Zheng, Y. S., (1997), Sensitivity analysis of an inventory model of type (s,S) inventory model, Operation Research and Letters, 21, pp. 19-23.
  • Embrechts, P., Kluppelberg, C., Mikosh, T., (1997), Modelling Extremal Events, Springer Verlag.
  • Feller, W., (1971), Introduction to Probability Theory and Its Applications II, John Wiley, New York.
  • Foss, S., Korshunov, D., Zachary, S., (2011), An Introduction to Heavy Tailed and Subexponential
  • Distributions, Springer Series in Operaions Research and Financial Engineering, New York. Gaffeo, Edoardo, Antonello, E. S., Laura, V., (2008), Demand distribution dynamics in creative industries: The market for books in Italy, Information Economics and Policy, 20 (3), pp. 257-268.
  • Geluk, J. L., (1997), A renewal theorem in the finite-mean case, Proceedings of the American Math- ematical Society, 125 (11), pp. 3407-3413.
  • Gikhman, I. I., Skorohod, A. V., (1975), Theory of Stochastic Processes II, Springer: Berlin.
  • Khaniyev, T., Aksop, C., (2011), Asymptotic results for an inventory model of type (s,S) with gener- alized beta interference of chance, TWMS J.App.Eng.Math., 2, pp. 223-236.
  • Khaniyev, T., 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), pp. 599-611.
  • Khaniyev, T., Kokangul, A., Aliyev, R. (2013), An asymptotic approach for a semi Markovian inven- tory model of type (s,S), Applied Stochastic Models in Business and Industry, 29 (5), pp. 439-453.
  • Levy, J., Taqqu, M. S, (1987), On renewal processes having stable inter-renewal intervals and stable rewards, Ann.Sci.Math., 11, pp. 95-110.
  • Resnick, S. I., (2006), Heavy-Tail Phenomena: Probabilistic and Statistical Madeling, Springer Series in Operations Research and Financial Engineering, New York.
  • Seneta, E., (1976), Regularly Varying Functions, Springer-Verlag, New York.
  • Sgibnev, M. S., (2009), On a renewal function when second moment is infinite, Statistics and Proba- bility Letters, 79, pp. 1242-1245.
  • Smith, W. L., (1959), On the cumulants of renewal process, Biometrika 46 (1), pp. 1-29.
  • Teugels, J. L., (1968), Renewal theorems when the second moment is infinite, The Annals of Mathe- matical Statistics 39 (4), pp. 1210-1219.
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

T. Kesemen Bu kişi benim

T. Khaniyev Bu kişi benim

Yayımlanma Tarihi 1 Eylül 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8 Sayı: 1.1

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