Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chance

Yazlr T., Kamlşllk A., Khaniyev T., Hanalioglu Z.

DEMONSTRATIO MATHEMATICA, cilt.58, sa.1, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 58 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1515/dema-2025-0153
  • Dergi Adı: DEMONSTRATIO MATHEMATICA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Linguistic Bibliography, zbMATH, Directory of Open Access Journals
  • Anahtar Kelimeler: ergodic distribution, generalized gamma distribution, moment-based approximation, renewal reward process
  • Recep Tayyip Erdoğan Üniversitesi Adresli: Evet

Özet

This study investigates the renewal reward process under the assumption that the random variables describing the discrete interference of chance follow a generalized gamma distribution. A moment-based approximation method is employed to derive novel results for the renewal function, enabling an approximation of the ergodic distribution of the process. Furthermore, the limiting distribution of the ergodic distribution is also derived. The theoretical findings are illustrated through a specific example in which the demand random variable eta 1 {\eta }_{1} is represented by a third-order Erlang distribution with parameter theta = 1 \theta =1 .