GammaIInv

Revision as of 16:16, 27 January 2016 by Lchrisman (talk | contribs) (Problem with definition, had .. = y.b instead of .. = y. Added graph, examples)


GammaIInv(y, a, b)

Returns the inverse of the incomplete Gamma function. The function returns the value x such that

GammaI(x, a, b) = y

«a» is the shape parameter, «b» is an optional scale factor that defaults to 1.

Examples

Index y := Sequence(0,0.98,0.01)
Variable a := [0.5, 1, 2, 5 ]
GammaIInv(y,a)
GammaIInv.png
GammaI( 12, 5, 2 ) → 0.7149
GammaIInv( 0.7149, 5, 2 ) → 12

GammaIInv( Uniform(0,1), a, b ) is equivalent to Gamma(a,b).

GetFract( Gamma(a,b), y ) is an approximation to GammaIInv(y,a,b), obtained via sampling. The former is subject to sampling error, with less error at increased sample sizes, whereas by using GammaIInv directly, sampling error is avoided entirely.

See Also

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