Geometric process
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In probability, statistics and related fields, the geometric process is a counting process, introduced by Lam in 1988.^{[1]} It is defined as
The geometric process. Given a sequence of nonnegative random variables :, if they are independent and the cdf of is given by for , where is a positive constant, then is called a geometric process (GP).
The GP has been widely applied in reliability engineering ^{[2]}
Below are some of its extensions.
 The α series process.^{[3]} Given a sequence of nonnegative random variables :, if they are independent and the cdf of is given by for , where is a positive constant, then is called an α series process.
 The threshold geometric process.^{[4]} A stochastic process is said to be a threshold geometric process (threshold GP), if there exists real numbers and integers such that for each , forms a renewal process.
 The doubly geometric process.^{[5]} Given a sequence of nonnegative random variables :, if they are independent and the cdf of is given by for , where is a positive constant and is a function of and the parameters in are estimable, and for natural number , then is called a doubly geometric process (DGP).
 The semigeometric process.^{[6]} Given a sequence of nonnegative random variables , if and the marginal distribution of is given by , where is a positive constant, then is called a semigeometric process
References[edit]
 ^ Lam, Y. (1988). Geometric processes and replacement problem. Acta Mathematicae Applicatae Sinica. 4, 366–377
 ^ Lam, Y. (2007). Geometric process and its applications. World Scientific, Singapore MATH. ISBN 9789812700032.
 ^ Braun, W. J., Li, W., & Zhao, Y. Q. (2005). Properties of the geometric and related processes. Naval Research Logistics (NRL), 52(7), 607–616.
 ^ Chan, J.S., Yu, P.L., Lam, Y. & Ho, A.P. (2006). Modelling SARS data using threshold geometric process. Statistics in Medicine. 25 (11): 1826–1839.
 ^ Wu, S. (2017). Doubly geometric processes and applications. Journal of the Operational Research Society, 1–13. doi:10.1057/s4127401702174.
 ^ Wu, S., Wang, G. (2017). The semigeometric process and some properties. IMA J Management Mathematics, 1–13.