| dbo:abstract
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- In probability, statistics and related fields, the geometric process is a counting process, introduced by Lam in 1988. 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 Below are some of its extensions.
* The α- series 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 an α- series process.
* The threshold geometric process. 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. 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. 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
* The double ratio geometric process. Given a sequence of non-negative random variables , if they are independent and the cdf of is given by for , where and are positive parameters (or ratios) and . We call the stochastic process the double-ratio geometric process (DRGP). (en)
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| rdfs:comment
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- In probability, statistics and related fields, the geometric process is a counting process, introduced by Lam in 1988. 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 Below are some of its extensions. (en)
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