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Journals / Contemporary Analysis and Applied Mathematics / 2013 / Cilt: 1 - Sayı: 2

Weibull dağılımlı şans girişimi ile yenileme-¨odül süreci için asimptotik açılımlar

Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance

Rovshan ALİYEV
Nurgül BEKAR OKUR
Tahir KHANİYEV
Pages
200–211
Publication Date
2022-10-11
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Based on these results, the asymptotic expansions are obtained for the skewness and kurtosis of the process X(t), as λ → 0.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, a renewal-reward process (X(t)) with a Weibull distributed interference of chance is investigated.
📊
Key Findings & Data:Under the assumption that the process X(t) is ergodic, two-term asymptotic expansion is obtained for the ergodic distiribution of the process X(t), as λ → 0.
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Conclusion & Impact:Based on these results, the asymptotic expansions are obtained for the skewness and kurtosis of the process X(t), as λ → 0.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this study, a renewal-reward process (X(t)) with a Weibull distributed interference of chance is investigated. Under the assumption that the process X(t) is ergodic, two-term asymptotic expansion is obtained for the ergodic distiribution of the process X(t), as λ → 0. Also, the weak convergence theorem is proved for the ergodic distribution of the process X(t), as λ → 0. Moreover, two-term asymptotic expansions are derived for n th-order moments n = 1, 2, ... of the process X(t), as λ → 0. Based on these results, the asymptotic expansions are obtained for the skewness and kurtosis of the process X(t), as λ → 0.

Özet

Bu çalışmada, Weibull dağılımlı şans girişimi ile bir yenileme-¨odül süreci (X(t)) incelendi. X(t) sürecinin ergodik olduğu kabulu altında λ → 0 iken X(t) sürecinin ergodik dağılımı için iki-terimli asimptotik açılım elde edildi. Aynı zamanda λ → 0 iken X(t) sürecinin ergodik dağılımı için zayıf yaklaşım teoremi ispatlandı. Dahası, λ → 0 iken X(t) sürecinin n.-mertebeden anları n = 1, 2, ... için iki-terimli asimptotik açılımlar çıkartıldı. Bu sonuçlara dayanarak X(t) sürecinin çarpıklık ve basıklıkları için asimptotik açılımlar elde edildi.

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Cite This Article

ALİYEV, R., OKUR, N. B., KHANİYEV, T. (2022). Weibull dağılımlı şans girişimi ile yenileme-¨odül süreci için asimptotik açılımlar. Contemporary Analysis and Applied Mathematics, Cilt: 1 - Sayı: 2, 200–211. https://ajindex.com/articles/476498

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