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An integral equation for the second moment function of a geometric process and its numerical solution
Author(s) -
Pekalp Mustafa Hilmi,
Aydoğdu Halil
Publication year - 2018
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21791
Subject(s) - mathematics , weibull distribution , exponential function , moment (physics) , integral equation , function (biology) , log normal distribution , mathematical analysis , exponential distribution , numerical integration , statistics , physics , classical mechanics , evolutionary biology , biology
In this article, an integral equation satisfied by the second moment function M 2 ( t ) of a geometric process is obtained. The numerical method based on the trapezoidal integration rule proposed by Tang and Lam for the geometric function M ( t ) is adapted to solve this integral equation. To illustrate the numerical method, the first interarrival time is assumed to be one of four common lifetime distributions, namely, exponential, gamma, Weibull, and lognormal. In addition to this method, a power series expansion is derived using the integral equation for the second moment function M 2 ( t ), when the first interarrival time has an exponential distribution.