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

OKUR, Nurgul; KHANIYEV, Tahir; ALIYEV, Rovshan

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

Nurgül BEKAR OKUR, (Giresun Üniversitesi, Fen Edebiyat Fakültesi, İstatistik Bölümü, Giresun, Türkiye)

Rovshan ALIYEV, (Baku State University, Faculty of Applied Mathematics and Cybernetics, Department of Probability Theory and Mathematical Statistics Z. Khalilov 23, Az 1148, Baku, Azerbaijan)

Tahir KHANIYEV (TOBB Ekonomi ve Teknoloji Üniversitesi, Endüstri Mühendisliği Bölümü, Ankara, Türkiye)

Contemporary Analysis and Applied Mathematics

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Yıl: 2013 Cilt: 1 Sayı: 2 Sayfa Aralığı: 200 - 211 Metin Dili: Türkçe İndeks Tarihi: 29-07-2022

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

Öz:

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.

Anahtar Kelime:

Konular: Matematik

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

Öz:

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.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

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APA	OKUR N, ALIYEV R, KHANIYEV T (2013). Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance. , 200 - 211.
Chicago	OKUR Nurgul,ALIYEV Rovshan,KHANIYEV Tahir Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance. (2013): 200 - 211.
MLA	OKUR Nurgul,ALIYEV Rovshan,KHANIYEV Tahir Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance. , 2013, ss.200 - 211.
AMA	OKUR N,ALIYEV R,KHANIYEV T Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance. . 2013; 200 - 211.
Vancouver	OKUR N,ALIYEV R,KHANIYEV T Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance. . 2013; 200 - 211.
IEEE	OKUR N,ALIYEV R,KHANIYEV T "Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance." , ss.200 - 211, 2013.
ISNAD	OKUR, Nurgul vd. "Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance". (2013), 200-211.

APA	OKUR N, ALIYEV R, KHANIYEV T (2013). Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance. Contemporary Analysis and Applied Mathematics, 1(2), 200 - 211.
Chicago	OKUR Nurgul,ALIYEV Rovshan,KHANIYEV Tahir Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance. Contemporary Analysis and Applied Mathematics 1, no.2 (2013): 200 - 211.
MLA	OKUR Nurgul,ALIYEV Rovshan,KHANIYEV Tahir Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance. Contemporary Analysis and Applied Mathematics, vol.1, no.2, 2013, ss.200 - 211.
AMA	OKUR N,ALIYEV R,KHANIYEV T Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance. Contemporary Analysis and Applied Mathematics. 2013; 1(2): 200 - 211.
Vancouver	OKUR N,ALIYEV R,KHANIYEV T Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance. Contemporary Analysis and Applied Mathematics. 2013; 1(2): 200 - 211.
IEEE	OKUR N,ALIYEV R,KHANIYEV T "Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance." Contemporary Analysis and Applied Mathematics, 1, ss.200 - 211, 2013.
ISNAD	OKUR, Nurgul vd. "Asymptotic expansions for a renewal-reward process with Weibull distributed interference of chance". Contemporary Analysis and Applied Mathematics 1/2 (2013), 200-211.