KaydedilenlerDerginizi ekleyin

Dergiler / TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics / 2018 / Cilt: 8 - Sayı: 2

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

ASLI BEKTAŞ KAMIŞLIK
TÜLAY KESEMEN
Tahir KHANIYEV
Sayfa
318–329
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Subsequently we consider this system with Pareto distributed demand random variables and apply obtained results in this special case.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez: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.
📊
Temel Bulgular & Veri:In order to obtain renewal function generated by the regularly varying random variables, we used a special asymptotic expansion provided by Geluk [14].
💡
Sonuç & Katkı:Subsequently we consider this system with Pareto distributed demand random variables and apply obtained results in this special case.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Özet

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 infinite 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 first step we investigate the current problem with the whole class of regularly varying distributions with tail parameter 1 <α< 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.

🔖

Bu Makaleye Atıf Yap

KAMIŞLIK, A. B., KESEMEN, T., KHANIYEV, T. (2018). ON THE MOMENTS FOR ERGODIC DISTRIBUTION OF AN INVENTORY MODEL OF TYPE (s, S) WITH REGULARLY VARYING DEMANDS HAVING INFINITE VARIANCE. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, Cilt: 8 - Sayı: 2, 318–329. https://ajindex.com/articles/327651

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (16)

  1. Aliyev, R. T., (2016), On a stochastic process with a heavy tailed distributed component describing inventory model of type (s,S), Communications in Statistics-Theory and Methods, DOI: 10.1080/03610926.2014.1002932. 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.
  2. 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.
  3. Asmussen, S., (2000),
  4. Ruin Probabilities, World Scientific Publishing, Singapore. Bingham, N. H., Goldie, C. M., Teugels, J. L., (1987),
  5. Regular Variation, Cambridge University Press,
  6. Cambridge. Borokov, A. A., Borokov, K. A., (2008),
  7. Asymptotic Analysis of Random Walks, Heavy Tailed Distributions, Cambridge University Press,
  8. 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.
  9. 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.
  10. 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.
  11. Embrechts, P., Kluppelberg, C., Mikosh, T., (1997),
  12. 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.
  13. Geluk, J. L., (1997), A renewal theorem in the finite-mean case, Proceedings of the American Mathematical Society, 125 (11), pp. 3407-3413.
  14. Gikhman, I. I., Skorohod, A. V., (1975),
  15. Theory of Stochastic Processes II, Springer: Berlin. Khaniyev, T., Aksop, C., (2011), Asymptotic results for an inventory model of type (s,S) with generalized beta interference of chance, TWMS J.App.Eng.Math., 2, pp. 223-236.
  16. Khaniyev, T., Atalay,