Difference between revisions of "GammaIInv"

Latest revision as of 21:16, 24 May 2016

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.

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.

Library

Advanced Math, Distribution Densities Library (Distribution Densities.ana)

Use File → Add Library... to add this library

Examples

Index y := Sequence(0,0.98, 0.01)

Variable a := [0.5, 1, 2, 5]

GammaIInv(y, a) →

GammaI(12, 5, 2) → 0.7149

GammaIInv(0.7149, 5, 2) → 12

@@ Line 1: / Line 1: @@
-[[category:Analytic Distribution Functions]]
+[[Category:Analytic Distribution Functions]]
-[[Category:Doc Status D]] <!-- For Lumina use, do not change -->
+[[Category: Distribution Densities library functions]]
-= GammaIInv(Y, A, B) =
+== GammaIInv(y, a, b) ==
-Returns the inverse of the gamma function. The function returns the value x such that
+Returns the inverse of the incomplete [[Gamma]] function. The function returns the value ''x'' such that
- GammaI(x, a, b) = y.b
+:[[GammaI]](x, a, b) = y
-''A'' is the shape parameter, ''B'' is an optional scale factor (default ''B=1'').  Note that some textbooks use <math>\lambda = 1/A</math>as the scale factor.  The incomplete gamma function is defined for <math>X\geq 0</math>.
+«a» is the shape parameter, «b» is an optional scale factor that defaults to 1.
-= Library =
+[[GammaIInv]]([[Uniform]](0, 1), a, b) is equivalent to [[Gamma]](a, b).
-Advanced Math
+[[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.
+== Library ==
+Advanced Math, [[Distribution Densities Library]]  ([[media:Distribution Densities.ana|Distribution Densities.ana]])
+:Use [[File menu|File]] &rarr; '''Add Library...''' to add this library
+== Examples ==
+:<code>Index y := Sequence(0,0.98, 0.01)</code>
+:<code>Variable a := [0.5, 1, 2, 5]</code>
+:<code>GammaIInv(y, a) &rarr;</code>
+:[[image:GammaIInv.png]]
+:<code>GammaI(12, 5, 2) &rarr; 0.7149 </code>
+:<code>GammaIInv(0.7149, 5, 2) &rarr; 12 </code>
+==See Also==
+* [[Gamma]]
+* [[GammaI]]
+* [[Distribution Densities Library]]
+* [[media:Distribution Densities.ana|Distribution Densities.ana]]