Difference between revisions of "GammaIInv"
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= GammaIInv(Y, A, B) =
 
= GammaIInv(Y, A, B) =
  
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Returns the incomplete gamma function, defined as:
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Returns the inverse of the gamma function. The function returns the value x such that
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:<math>GammaI(X,A,B) = {1\over{\gamma(A)}} \int_0^{x/B} e^{-t} t^{A-1} dt</math>
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GammaI(x, a, b) = y.b
  
 
''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 (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>.
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The incomplete gamma function returns the cumulative area from zero to ''X'' under the [[Gamma]] distribution.
 
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The incomplete gamma function is useful in a number of mathematical and statistical contexts.
 
  
 
= Library =
 
= Library =
  
 
Advanced Math
 
Advanced Math

Revision as of 01:29, 17 February 2010


GammaIInv(Y, A, B)

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

GammaI(x, a, b) = y.b

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].

Library

Advanced Math

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