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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