dcgamma
approximates density of a gamma shape distribution with
a gamma density. rcgamma
obtains random draws from the
approximation. mcgamma
computes approximated mean, variance and
normalization constant.
1 2 3 |
x |
Vector indicating the values at which to evaluate the density. |
n |
Number of random draws to obtain. |
a,b,c,d,r,s |
Parameter values. |
newton |
Set to |
The density of a gamma shape distribution is given by
C(a,b,c,d,r,s) (gamma(a*x+d)/gamma(x)^a)
(x/(r+s*x))^{a*x+d} x^{b-d-1} exp(-x*c)
for x>=0
, and 0 otherwise, where C()
is the normalization constant.
The gamma approximation is
Ga(a/2+b-1/2,c+a*log(s/a))
. The approximate normalization constant is
obtained by taking the ratio of the exact density and the
approximation at the maximum, as described in Rossell (2007).
dcgamma
returns a vector with approximate density.
rcgamma
returns a vector with draws from the approximating gamma.
mcgamma
returns a list with components:
m |
Approximate mean |
v |
Approximate variance |
normk |
Approximate normalization constant |
For general values of the parameters the gamma approximation may be poor. In such a case one could use this function to obtain draws from the proposal distribution in a Metropolis-Hastings step.
David Rossell
Rossell D. GaGa: a simple and flexible hierarchical model for microarray data analysis. http://rosselldavid.googlepages.com.
dgamma
, rgamma
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