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

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 appr...

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Main Authors: Yazır Tülay, Kamışlık Aslı Bektaş, Khaniyev Tahir, Hanalioglu Zulfiye
Format: Article
Language:English
Published: De Gruyter 2025-07-01
Series:Demonstratio Mathematica
Subjects:
Online Access:https://doi.org/10.1515/dema-2025-0153
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author Yazır Tülay
Kamışlık Aslı Bektaş
Khaniyev Tahir
Hanalioglu Zulfiye
author_facet Yazır Tülay
Kamışlık Aslı Bektaş
Khaniyev Tahir
Hanalioglu Zulfiye
author_sort Yazır Tülay
collection DOAJ
description 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 η1{\eta }_{1} is represented by a third-order Erlang distribution with parameter θ=1\theta =1.
format Article
id doaj-art-ceccc623be114490922a6cf92f841223
institution Kabale University
issn 2391-4661
language English
publishDate 2025-07-01
publisher De Gruyter
record_format Article
series Demonstratio Mathematica
spelling doaj-art-ceccc623be114490922a6cf92f8412232025-08-20T03:43:14ZengDe GruyterDemonstratio Mathematica2391-46612025-07-0158136137210.1515/dema-2025-0153Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chanceYazır Tülay0Kamışlık Aslı Bektaş1Khaniyev Tahir2Hanalioglu Zulfiye3Department of Mathematics, Karadeniz Technical University, Trabzon, TurkeyDepartment of Mathematics, Recep Tayyip Erdogan University, Rize, TurkeyDepartment of Industrial Engineering, TOBB Economics and Technology University, Ankara, TurkeyDepartment of Actuarial Sciences, Karabuk University, Karabuk, TurkeyThis 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 η1{\eta }_{1} is represented by a third-order Erlang distribution with parameter θ=1\theta =1.https://doi.org/10.1515/dema-2025-0153moment-based approximationergodic distributionrenewal reward processgeneralized gamma distribution60k0560k15
spellingShingle Yazır Tülay
Kamışlık Aslı Bektaş
Khaniyev Tahir
Hanalioglu Zulfiye
Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chance
Demonstratio Mathematica
moment-based approximation
ergodic distribution
renewal reward process
generalized gamma distribution
60k05
60k15
title Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chance
title_full Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chance
title_fullStr Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chance
title_full_unstemmed Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chance
title_short Moment-based approximation for a renewal reward process with generalized gamma-distributed interference of chance
title_sort moment based approximation for a renewal reward process with generalized gamma distributed interference of chance
topic moment-based approximation
ergodic distribution
renewal reward process
generalized gamma distribution
60k05
60k15
url https://doi.org/10.1515/dema-2025-0153
work_keys_str_mv AT yazırtulay momentbasedapproximationforarenewalrewardprocesswithgeneralizedgammadistributedinterferenceofchance
AT kamıslıkaslıbektas momentbasedapproximationforarenewalrewardprocesswithgeneralizedgammadistributedinterferenceofchance
AT khaniyevtahir momentbasedapproximationforarenewalrewardprocesswithgeneralizedgammadistributedinterferenceofchance
AT hanaliogluzulfiye momentbasedapproximationforarenewalrewardprocesswithgeneralizedgammadistributedinterferenceofchance