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Journals / Gümüşhane Üniversitesi Fen Bilimleri Dergisi / 2018 / Cilt: 8 Sayı: 2

Estimators of the Moments for a Semi- Markovian Model of Type (s,S) With a Triangular Distributed Interference of Chance

Üçgensel Müdahaleli Yarı- Markov (s,S) Tipli Modellerin Momentleri İçin Tahmin Ediciler

Tülay KESEMEN
Melek ERİŞ BÜYÜKKAYA
Aslı BEKTAŞ KAMIŞLIK
Pages
430–441
Publication Date
2018-07-31
DOI
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AI Summary & Key Takeaways

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

Moreover statistical properties such as consistency, asymptotic unbiasedness and asymptotic normality were investigated for the obtained estimator, respectively.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study inventory model of type (s,S) with triangular interference of chance has been investigated by using renewal process and the statistical estimator problem for moments of ergodic distribution of the process which define the model has been obtained.
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Key Findings & Data:The main motivation of this study is the publication by Frees (1986 b) in which he proposed a statistical estimator for the renewal function.
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Conclusion & Impact:Moreover statistical properties such as consistency, asymptotic unbiasedness and asymptotic normality were investigated for the obtained estimator, respectively.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Asimptotik Normallik · Asimptotik Yansızlık · İstatistiksel tahmin edici

Abstract

In this study inventory model of type (s,S) with triangular interference of chance has been investigated by using renewal process and the statistical estimator problem for moments of ergodic distribution of the process which define the model has been obtained. Different estimators for the renewal function are available in the literature, when the distribution which defines the time between renewals is not known precisely. The main motivation of this study is the publication by Frees (1986 b) in which he proposed a statistical estimator for the renewal function. By using the estimator by Frees (1986 b) we obtained a new estimator for the moments of ergodic distribution function of the process describing inventory model of type (s,S). Moreover statistical properties such as consistency, asymptotic unbiasedness and asymptotic normality were investigated for the obtained estimator, respectively.

Özet

Bu çalışmada üçgensel müdahaleli (s,S) tipli yarı-Markov bir envanter(stok kontrol) model yenileme süreci ele alınmış, ve bu sürecin ergodik dağılımının momentleri için tahmin edici problemi araştırılmıştır. Yenileme süreçlerinde, yenilemeler arasında geçen sürenin dağılımı tam olarak bilinmediğinde yenileme fonksiyonu için tahmin ediciler literatürde mevcuttur. Bu çalışmanın ana motivasyonu ise, Frees (1986 b) tarafından yenileme fonksiyonu için önerilmiş tahmin edicidir. Bu amaçla Frees (1986 b)’ in yaklaşımı kullanılarak ele alınan modelin ergodik dağılımının momentleri için istatistiksel bir tahmin edici bulunmuş ve bu tahmin edici için sırasıyla tutarlılık, asimptotik yansızlık ve asimptotik normallik gibi istatistiksel özellikler araştırılmıştır.

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Cite This Article

KESEMEN, T., BÜYÜKKAYA, M. E., KAMIŞLIK, A. B. (2018). Estimators of the Moments for a Semi- Markovian Model of Type (s,S) With a Triangular Distributed Interference of Chance. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, Cilt: 8 Sayı: 2, 430–441. https://ajindex.com/articles/928786

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References (12)

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