Difference between revisions of "GammaIInv"
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− | [[ | + | [[Category:Analytic Distribution Functions]] |
− | [[Category: | + | [[Category: Distribution Densities library functions]] |
− | = GammaIInv( | + | == GammaIInv(y, a, b) == |
− | Returns the incomplete | + | 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). | |
− | The | + | [[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 = | + | == Library == |
+ | Advanced Math, [[Distribution Densities Library]] ([[media:Distribution Densities.ana|Distribution Densities.ana]]) | ||
+ | :Use [[File menu|File]] → '''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) →</code> | ||
+ | |||
+ | :[[image:GammaIInv.png]] | ||
+ | |||
+ | :<code>GammaI(12, 5, 2) → 0.7149 </code> | ||
+ | :<code>GammaIInv(0.7149, 5, 2) → 12 </code> | ||
+ | |||
+ | ==See Also== | ||
+ | * [[Gamma]] | ||
+ | * [[GammaI]] | ||
+ | * [[Distribution Densities Library]] | ||
+ | * [[media:Distribution Densities.ana|Distribution Densities.ana]] |
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
See Also
Comments
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