Under this assumption, the ergodicity of this process is discussed andthe asymptotic expansions with three terms for the first four momentsof the ergodic distribution of the process X(t) are derived, when λ → 0.Moreover, the asymptotic expansions for the skewness and kurtosis ofthe ergodic distribution of the process X(t) are established.
📌 3 Maddede Bu Makale
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Amaç & Hipotez:In this paper, a semi-Markovian random walk with delay and a discreteinterference of chance (X(t)) is considered.
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Temel Bulgular & Veri:It is assumed that therandom variables {ζn} , n ≥ 1 which describe the discrete interferenceof chance have Weibull distribution with parameters (α, λ), α > 1, λ >0.
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Sonuç & Katkı:Under this assumption, the ergodicity of this process is discussed andthe asymptotic expansions with three terms for the first four momentsof the ergodic distribution of the process X(t) are derived, when λ → 0.Moreover, the asymptotic expansions for the skewness and kurtosis ofthe ergodic distribution of the process X(t) are established.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri
Abstract
In this paper, a semi-Markovian random walk with delay and a discreteinterference of chance (X(t)) is considered. It is assumed that therandom variables {ζn} , n ≥ 1 which describe the discrete interferenceof chance have Weibull distribution with parameters (α, λ), α > 1, λ >0. Under this assumption, the ergodicity of this process is discussed andthe asymptotic expansions with three terms for the first four momentsof the ergodic distribution of the process X(t) are derived, when λ → 0.Moreover, the asymptotic expansions for the skewness and kurtosis ofthe ergodic distribution of the process X(t) are established.
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Bu Makaleye Atıf Yap
KESEMEN, T. (2022). ON THE SEMI-MARKOVIAN RANDOM WALK WITH DELAY AND WEIBULL DISTRIBUTED INTERFERENCE OF CHANCE. Hacettepe Journal of Mathematics and Statistics, Cilt: 42 - Sayı: 3, 299–307. https://ajindex.com/articles/530420
Aliyev, R.T., Khaniyev, T.A and Kesemen, T. Asymptotic expansions for the moments of a semi-Markovian random walk with gamma distributed interference of chance, Communications in Statistics-Theory and Methods, 39 (1), 130–143, 2010
Aliyev, R., Kucuk, Z. and Khaniyev, T. Three-term asymptotic expansions for the moments of the random walk with triangular distributed interference of chance, Applied Mathematical Modelling, 34 (11), 3599–3607, 2010
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