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The gamma distribution (;) (>) can be expressed as the product distribution of a Weibull distribution and a variant form of the stable count distribution. Its shape parameter can be regarded as the inverse of Lévy's stability parameter in the stable count distribution: (;) = [()], where () is a standard stable count distribution of shape , and ...
In probability theory and statistics, a shape parameter (also known as form parameter) [1] is a kind of numerical parameter of a parametric family of probability distributions [2] that is neither a location parameter nor a scale parameter (nor a function of these, such as a rate parameter).
It is a generalization of the gamma distribution which has one shape parameter (and a scale parameter). Since many distributions commonly used for parametric models in survival analysis (such as the exponential distribution , the Weibull distribution and the gamma distribution ) are special cases of the generalized gamma, it is sometimes used ...
The Gamma distribution, which describes the time until n consecutive rare random events occur in a process with no memory. The Erlang distribution, which is a special case of the gamma distribution with integral shape parameter, developed to predict waiting times in queuing systems; The inverse-gamma distribution; The generalized gamma distribution
with shape parameter and scale parameter. [2] Here () denotes the gamma function. Unlike the gamma distribution, which contains a somewhat similar exponential term, is a scale parameter as the density function satisfies:
A Weibull distribution is a generalized gamma distribution with both shape parameters equal to k. The translated Weibull distribution (or 3-parameter Weibull) contains an additional parameter. [ 12 ] It has the probability density function
Also known as the (Moran-)Gamma Process, [1] the gamma process is a random process studied in mathematics, statistics, probability theory, and stochastics. The gamma process is a stochastic or random process consisting of independently distributed gamma distributions where N ( t ) {\displaystyle N(t)} represents the number of event occurrences ...
The Nakagami distribution or the Nakagami-m distribution is a probability distribution related to the gamma distribution. The family of Nakagami distributions has two parameters: a shape parameter / and a scale parameter >. It is used to model physical phenomena such as those found in medical ultrasound imaging, communications engineering ...