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

Year 2018, , 430 - 441, 31.07.2018

Tülay Kesemen Melek Eriş Büyükkaya Aslı Bektaş Kamışlık

https://doi.org/10.17714/gumusfenbil.396957

Abstract

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.

Keywords

Asimptotik Normallik, Asimptotik Yansızlık, İstatistiksel tahmin edici, (sS) tipli yarı-Markow envanter model, Tutarlılık

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

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.

Keywords

Inventory model of type (s S), Asymptotic Normality, Asymptotic Unbiasedness, Statistical estimators, Consistency

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