Geometric process

• 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, 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.
• 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