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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| Format: | Article |
| Language: | English |
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De Gruyter
2025-07-01
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| Series: | Demonstratio Mathematica |
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| Online Access: | https://doi.org/10.1515/dema-2025-0153 |
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| _version_ | 1849342872989466624 |
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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 |