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- function x = spm_invXcdf(F,v)
- % Inverse Cumulative Distribution Function (CDF) of Chi-squared distribution
- % FORMAT x = spm_invXcdf(F,v)
- %
- % F - CDF (lower tail p-value)
- % v - degrees of freedom (v>0, non-integer d.f. accepted)
- % x - Chi-squared ordinates at which CDF F(x)=F
- %__________________________________________________________________________
- %
- % spm_invXcdf implements the inverse Cumulative Distribution of the
- % Chi-squared distribution.
- %
- % Definition:
- %--------------------------------------------------------------------------
- % The Chi-squared distribution with v degrees of freedom is defined for
- % positive integer v and x in [0,Inf). The Cumulative Distribution
- % Function (CDF) F(x) is the probability that a realisation of a
- % Chi-squared random variable X has value less than x. F(x)=Pr{X<x}:
- % (See Evans et al., Ch8)
- %
- % Variate relationships: (Evans et al., Ch8 & Ch18)
- %--------------------------------------------------------------------------
- % The Chi-squared distribution with v degrees of freedom is equivalent to
- % the Gamma distribution with scale parameter 1/2 and shape parameter v/2.
- %
- % Algorithm:
- %--------------------------------------------------------------------------
- % Using routine spm_invGcdf for Gamma distribution, with appropriate
- % parameters.
- %
- % References:
- %--------------------------------------------------------------------------
- % Evans M, Hastings N, Peacock B (1993)
- % "Statistical Distributions"
- % 2nd Ed. Wiley, New York
- %
- % Abramowitz M, Stegun IA, (1964)
- % "Handbook of Mathematical Functions"
- % US Government Printing Office
- %
- % Press WH, Teukolsky SA, Vetterling AT, Flannery BP (1992)
- % "Numerical Recipes in C"
- % Cambridge
- %
- %__________________________________________________________________________
- % Copyright (C) 1993-2011 Wellcome Trust Centre for Neuroimaging
- % Andrew Holmes
- % $Id: spm_invXcdf.m 4182 2011-02-01 12:29:09Z guillaume $
- %-Check enough arguments
- %--------------------------------------------------------------------------
- if nargin<2, error('Insufficient arguments'), end
- %-Computation
- %--------------------------------------------------------------------------
- x = spm_invGcdf(F,v/2,1/2);
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