Geometric process

In probability, statistics and related fields, the geometric process is a counting process, introduced by Lam in 1988. It is defined as 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 : { X k , k = 1 , 2 , … } {displaystyle {X_{k},k=1,2,dots }} , if they are independent and the cdf of X k {displaystyle X_{k}} is given by F ( a k − 1 x ) {displaystyle F(a^{k-1}x)} for k = 1 , 2 , … {displaystyle k=1,2,dots } , where a {displaystyle a} is a positive constant, then { X k , k = 1 , 2 , … } {displaystyle {X_{k},k=1,2,ldots }} is called a geometric process (GP). The GP has been widely applied in reliability engineering