Numerical solution to an integral equation for the kth moment function of a geometric process

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Atıf İçin Kopyala

PEKALP M. H., Aydoğdu A.

Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, cilt.70, sa.2, ss.731-743, 2021 (ESCI)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 70 Sayı: 2
• Basım Tarihi: 2021
• Doi Numarası: 10.31801/cfsuasmas.865647
• Dergi Adı: Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
• Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.731-743
• Anahtar Kelimeler: Geometric process, moment functions, skewness and kurtosis, numerical solution, QUASI-RENEWAL PROCESS
• Ankara Üniversitesi Adresli: Evet

Özet

In this paper, an integral equation for the kth moment function of a geometric process is derived as a generalization of the lower-order moments of the process. We propose a general solution to solve this integral equation by using the numerical method, namely trapezoidal integration rule. The general solution is reduced to the numerical solution of the integral equations which will be given for the third and fourth moment functions to compute the skewness and kurtosis of a geometric process. To illustrate the numerical method, we assume gamma, Weibull and lognormal distributions for the first interarrival time of the geometric process.