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Analysis and Simulation of Lucas Distribution Using Markov Chain Monte Carlo Methods   
Yazarlar (2)
Abd Anasır Edabaa
Prof. Dr. Göksal BİLGİCİ Prof. Dr. Göksal BİLGİCİ
Kastamonu Üniversitesi, Türkiye
Devamını Göster
Özet
This study aims to investigate the properties of the Lucas distribution and apply the Markov Chain Monte Carlo (MCMC) method to simulate it and estimate its statistical characteristics. The work begins by defining the probability mass function of the Lucas distribution and establishing its mathematical connection to Birth–Death processes in continuous-time Markov chains. A generator matrix is constructed, and the corresponding discrete-time transition matrix is derived, demonstrating that the stationary distribution matches the target Lucas distribution. The Metropolis–Hasting’s algorithm is then implemented in the R programming environment to generate samples from this distribution. The simulated results are analyzed and compared with theoretical values through graphical and statistical summaries. The findings reveal a high degree of agreement between the estimated and theoretical values over most of the range, with noticeable underrepresentation in the upper tail, suggesting the need for improved proposal mechanisms or longer chains. This research provides both a mathematical framework and an applied methodology for using MCMC to simulate uncommon discrete distributions and offers methodological enhancements to overcome the observed limitations.
Anahtar Kelimeler
Makale Türü Özgün Makale
Makale Alt Türü SCOPUS dergilerinde yayınlanan tam makale
Dergi Adı Libyan Journal of Medical and Applied Sciences
Dergi ISSN 3006-1113
Dergi Tarandığı Indeksler Scopus
Makale Dili Türkçe
Basım Tarihi 08-2025
Cilt No 3
Sayı 3
Sayfalar 48 / 56
Doi Numarası 10.64943/ljmas.v3i3.125
Makale Linki https://doi.org/10.64943/ljmas.v3i3.125
BM Sürdürülebilir Kalkınma Amaçları
Atıf Sayıları
Analysis and Simulation of Lucas Distribution Using Markov Chain Monte Carlo Methods

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