Moment-based approximations for stochastic control model of type (s, S)

Kamışlık A. B., Baghezze F., KESEMEN T., Khaniyev T.

Communications in Statistics - Theory and Methods, 2023 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2023
  • Doi Number: 10.1080/03610926.2023.2268765
  • Journal Name: Communications in Statistics - Theory and Methods
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Computer & Applied Sciences, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Keywords: moment-based approximation, renewal reward process, Stochastic control model of type (s S)
  • Recep Tayyip Erdoğan University Affiliated: Yes


In this study, we propose an approximation for a renewal reward process that describes a stochastic control model of type (s, S) based on the first three moments of demand random variables. Various asymptotic expansions for this model exist in the literature. All these studies rely on the condition of knowing the distribution function of demand random variables and require obtaining the asymptotic expansion of the renewal function produced by them. However, obtaining a renewal function can be challenging for certain distribution families, and in some cases, the mathematical structure of the renewal function is difficult to apply. Therefore, in this study, simple and compact approximations are presented for the stochastic control model of type (s, S). The findings of this study rely on Kambo’s method, through which we obtain approximations for the ergodic distribution, and the n th order ergodic moments of this process. To conclude the study, the accuracy of the proposed approximate formulas are examined through a specialized illustrative example. Moreover, it has been noted that the proposed approximation is more accurate than the approximations existing in the literature.