GammaI

GammaI(x,a,b)

Returns the incomplete gamma function, defined as:

[math]\displaystyle{ GammaI(x,a,b) = {1\over{\gamma(a)}} \int_0^{x/b} e^{-t} t^{a-1} dt }[/math]

«a» is the shape parameter, «b» is an optional scale factor (default b=1). Note that some textbooks use [math]\displaystyle{ \lambda = 1/a }[/math] as the scale factor. The incomplete gamma function is defined for [math]\displaystyle{ x\geq 0 }[/math].

The incomplete gamma function returns the cumulative area from zero to «x»' under the Gamma distribution.

The incomplete gamma function is useful in a number of mathematical and statistical contexts.

Library

Advanced Math

See Also

• GammaFn, LGamma -- the complete gamma function
• Gamma -- the gamma distribution
• GammaIInv -- the inverse of GammaI
• BetaI -- the incomplete beta function