Statistics Definitions > Gamma Function
The Gamma function (sometimes called the Euler Gamma function) is related to factorials by the following formula:
Γ(n) = (x – 1)!.
In other words, the gamma function is equal to the factorial function. However, while the factorial function is only defined for non-negative integers, the gamma can handle fractions as well as complex numbers.
The multivariate gamma function (MGF) is an extension of the gamma function for multiple variables. While the gamma function can only handle one input (“x”), the multivariate version can handle many. It is usually defined as:
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