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词条 Geometric process
释义

  1. References

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 non-negative 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 non-negative 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 non-negative 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 semi-geometric process. [6] Given a sequence of non-negative random variables , if and the marginal distribution of is given by , where is a positive constant, then is called a semi-geometric process

References

1. ^Lam, Y. (1988). [https://dx.doi.org/10.1007/BF02007241 Geometric processes and replacement problem]. Acta Mathematicae Applicatae Sinica. 4, 366–377
2. ^Lam, Y. (2007). Geometric process and its applications. World Scientific, Singapore MATH. {{ISBN|978-981-270-003-2}}.
3. ^Braun, W. J., Li, W., & Zhao, Y. Q. (2005). [https://dx.doi.org/10.1002/nav.20099 Properties of the geometric and related processes]. Naval Research Logistics (NRL), 52(7), 607–616.
4. ^Chan, J.S., Yu, P.L., Lam, Y. & Ho, A.P. (2006). [https://dx.doi.org/10.1002/sim.2376 Modelling SARS data using threshold geometric process]. Statistics in Medicine. 25 (11): 1826–1839.
5. ^Wu, S. (2017). [https://dx.doi.org/10.1057/s41274-017-0217-4 Doubly geometric processes and applications]. Journal of the Operational Research Society, 1–13. {{doi|10.1057/s41274-017-0217-4}}.
6. ^Wu, S., Wang, G. (2017). [https://academic.oup.com/imaman/article/doi/10.1093/imaman/dpx002/3829520/The-semigeometric-process-and-some-properties?guestAccessKey=eaf4f88c-24d4-4791-9e28-607b8a460d12 The semi-geometric process and some properties]. IMA J Management Mathematics, 1–13.
{{Stochastic processes}}

3 : Point processes|Markov processes|Poisson point processes
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