PURPOSE: a matrix of random draws from the gamma distribution
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USAGE: r = gamm_rnd(n,m,k)
where: n = the size of the vector drawn
m = a parameter such that the mean of the gamma = m/k
k = a parameter such that the variance of the gamma = m/(k^2)
note: m=r/2, k=2 equals chisq r random deviate
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RETURNS:
r = an n x 1 vector of random numbers from the gamma distribution
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SEE ALSO: gamm_inv, gamm_pdf, gamm_cdf
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NOTE: written by: Michael Gordy, 15 Sept 1993
mbgordy@athena.mit.edu
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REFERENCES: Luc Devroye, Non-Uniform Random Variate Generation,
New York: Springer Verlag, 1986, ch 9.3-6.0001 function gb = gamm_rnd(nrow,m,k) 0002 % PURPOSE: a matrix of random draws from the gamma distribution 0003 %--------------------------------------------------- 0004 % USAGE: r = gamm_rnd(n,m,k) 0005 % where: n = the size of the vector drawn 0006 % m = a parameter such that the mean of the gamma = m/k 0007 % k = a parameter such that the variance of the gamma = m/(k^2) 0008 % note: m=r/2, k=2 equals chisq r random deviate 0009 %--------------------------------------------------- 0010 % RETURNS: 0011 % r = an n x 1 vector of random numbers from the gamma distribution 0012 % -------------------------------------------------- 0013 % SEE ALSO: gamm_inv, gamm_pdf, gamm_cdf 0014 %--------------------------------------------------- 0015 % NOTE: written by: Michael Gordy, 15 Sept 1993 0016 % mbgordy@athena.mit.edu 0017 %--------------------------------------------------- 0018 % REFERENCES: Luc Devroye, Non-Uniform Random Variate Generation, 0019 % New York: Springer Verlag, 1986, ch 9.3-6. 0020 0021 if nargin ~= 3 0022 error('Wrong # of arguments to gamm_rnd'); 0023 end; 0024 0025 ncol = 1; 0026 gb=zeros(nrow,ncol); 0027 if m<=1 0028 % Use RGS algorithm by Best, p. 426 0029 c=1/m; 0030 t=0.07+0.75*sqrt(1-m); 0031 b=1+exp(-t)*m/t; 0032 for i1=1:nrow 0033 for i2=1:ncol 0034 accept=0; 0035 while accept==0 0036 u=rand; w=rand; v=b*u; 0037 if v<=1 0038 x=t*(v^c); 0039 accept=((w<=((2-x)/(2+x))) | (w<=exp(-x))); 0040 else 0041 x=-log(c*t*(b-v)); 0042 y=x/t; 0043 accept=(((w*(m+y-m*y))<=1) | (w<=(y^(m-1)))); 0044 end 0045 end 0046 gb(i1,i2)=x; 0047 end 0048 end 0049 else 0050 % Use Best's rejection algorithm XG, p. 410 0051 b=m-1; 0052 c=3*m-0.75; 0053 for i1=1:nrow 0054 for i2=1:ncol 0055 accept=0; 0056 while accept==0 0057 u=rand; v=rand; 0058 w=u*(1-u); y=sqrt(c/w)*(u-0.5); 0059 x=b+y; 0060 if x >= 0 0061 z=64*(w^3)*v*v; 0062 accept=(z<=(1-2*y*y/x)) ... 0063 | (log(z)<=(2*(b*log(x/b)-y))); 0064 end 0065 end 0066 gb(i1,i2)=x; 0067 end 0068 end 0069 end 0070 gb=gb/k; 0071 0072