simtb_spm_Gpdf() - Probability Density Function (PDF) of a Gamma distribution
FORMAT f = spm_Gpdf(g,h,l)
x - Gamma-variate (Gamma has range [0,Inf) )
h - Shape parameter (h>0)
l - Scale parameter (l>0)
f - PDF of Gamma-distribution with shape & scale parameters h & l
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spm_Gpdf implements the Probability Density Function of the Gamma
distribution.
Definition:
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The PDF of the Gamma distribution with shape parameter h and scale l
is defined for h>0 & l>0 and for x in [0,Inf) by: (See Evans et al.,
Ch18, but note that this reference uses the alternative
parameterisation of the Gamma with scale parameter c=1/l)
l^h * x^(h-1) exp(-lx)
f(x) = ---------------------
gamma(h)
Variate relationships: (Evans et al., Ch18 & Ch8)
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For natural (strictly +ve integer) shape h this is an Erlang distribution.
The Standard Gamma distribution has a single parameter, the shape h.
The scale taken as l=1.
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:
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Direct computation using logs to avoid roundoff errors.
References:
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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
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Copyright (C) 2005 Wellcome Department of Imaging Neuroscience