Numerical solution to an integral equation for the kth moment function of a geometric process
Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics, vol.70, no.2, pp.731-743, 2021 (ESCI, TRDizin)
- Publication Type: Article / Article
- Volume: 70 Issue: 2
- Publication Date: 2021
- Doi Number: 10.31801/cfsuasmas.865647
- Journal Name: Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics
- Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
- Page Numbers: pp.731-743
- Keywords: Geometric process, moment functions, skewness and kurtosis, numerical solution, QUASI-RENEWAL PROCESS
- Ankara University Affiliated: Yes
Abstract
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.