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

Authors : Mustafa Hilmi PEKALP, Ayşenur AYDOĞDU

Pages : 731-743

Doi:10.31801/cfsuasmas.865647

View : 21 | Download : 11

Publication Date : 2021-12-31

Article Type : Research Paper

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.
Keywords : Geometric process, moment functions, skewness and kurtosis, numerical solution