135 lines
6.9 KiB
HTML
135 lines
6.9 KiB
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<title>Description of gamm_rnd</title>
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<meta name="description" content="PURPOSE: a matrix of random draws from the gamma distribution">
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<div><a href="../index.html">Home</a> > <a href="index.html">.</a> > gamm_rnd.m</div>
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<!--<table width="100%"><tr><td align="left"><a href="../index.html"><img alt="<" border="0" src="../left.png"> Master index</a></td>
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<td align="right"><a href="index.html">Index for . <img alt=">" border="0" src="../right.png"></a></td></tr></table>-->
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<h1>gamm_rnd
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</h1>
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<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>PURPOSE: a matrix of random draws from the gamma distribution</strong></div>
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<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>function gb = gamm_rnd(nrow,m,k) </strong></div>
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<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre class="comment"> PURPOSE: a matrix of random draws from the gamma distribution
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---------------------------------------------------
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USAGE: r = gamm_rnd(n,m,k)
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where: n = the size of the vector drawn
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m = a parameter such that the mean of the gamma = m/k
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k = a parameter such that the variance of the gamma = m/(k^2)
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note: m=r/2, k=2 equals chisq r random deviate
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---------------------------------------------------
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RETURNS:
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r = an n x 1 vector of random numbers from the gamma distribution
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--------------------------------------------------
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SEE ALSO: gamm_inv, gamm_pdf, gamm_cdf
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---------------------------------------------------
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NOTE: written by: Michael Gordy, 15 Sept 1993
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mbgordy@athena.mit.edu
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---------------------------------------------------
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REFERENCES: Luc Devroye, Non-Uniform Random Variate Generation,
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New York: Springer Verlag, 1986, ch 9.3-6.</pre></div>
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<!-- crossreference -->
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<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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This function calls:
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<ul style="list-style-image:url(../matlabicon.gif)">
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</ul>
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This function is called by:
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<ul style="list-style-image:url(../matlabicon.gif)">
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<li><a href="beta_rnd.html" class="code" title="function rnd = beta_rnd (n, a, b)">beta_rnd</a> PURPOSE: random draws from the beta(a,b) distribution</li><li><a href="rndprior.html" class="code" title="function y = rndprior(bayestopt_)">rndprior</a> </li></ul>
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<!-- crossreference -->
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<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function gb = gamm_rnd(nrow,m,k)</a>
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0002 <span class="comment">% PURPOSE: a matrix of random draws from the gamma distribution</span>
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0003 <span class="comment">%---------------------------------------------------</span>
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0004 <span class="comment">% USAGE: r = gamm_rnd(n,m,k)</span>
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0005 <span class="comment">% where: n = the size of the vector drawn</span>
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0006 <span class="comment">% m = a parameter such that the mean of the gamma = m/k</span>
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0007 <span class="comment">% k = a parameter such that the variance of the gamma = m/(k^2)</span>
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0008 <span class="comment">% note: m=r/2, k=2 equals chisq r random deviate</span>
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0009 <span class="comment">%---------------------------------------------------</span>
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0010 <span class="comment">% RETURNS:</span>
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0011 <span class="comment">% r = an n x 1 vector of random numbers from the gamma distribution</span>
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0012 <span class="comment">% --------------------------------------------------</span>
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0013 <span class="comment">% SEE ALSO: gamm_inv, gamm_pdf, gamm_cdf</span>
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0014 <span class="comment">%---------------------------------------------------</span>
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0015 <span class="comment">% NOTE: written by: Michael Gordy, 15 Sept 1993</span>
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0016 <span class="comment">% mbgordy@athena.mit.edu</span>
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0017 <span class="comment">%---------------------------------------------------</span>
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0018 <span class="comment">% REFERENCES: Luc Devroye, Non-Uniform Random Variate Generation,</span>
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0019 <span class="comment">% New York: Springer Verlag, 1986, ch 9.3-6.</span>
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0020
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0021 <span class="keyword">if</span> nargin ~= 3
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0022 error(<span class="string">'Wrong # of arguments to gamm_rnd'</span>);
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0023 <span class="keyword">end</span>;
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0024
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0025 ncol = 1;
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0026 gb=zeros(nrow,ncol);
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0027 <span class="keyword">if</span> m<=1
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0028 <span class="comment">% Use RGS algorithm by Best, p. 426</span>
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0029 c=1/m;
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0030 t=0.07+0.75*sqrt(1-m);
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0031 b=1+exp(-t)*m/t;
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0032 <span class="keyword">for</span> i1=1:nrow
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0033 <span class="keyword">for</span> i2=1:ncol
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0034 accept=0;
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0035 <span class="keyword">while</span> accept==0
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0036 u=rand; w=rand; v=b*u;
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0037 <span class="keyword">if</span> v<=1
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0038 x=t*(v^c);
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0039 accept=((w<=((2-x)/(2+x))) | (w<=exp(-x)));
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0040 <span class="keyword">else</span>
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0041 x=-log(c*t*(b-v));
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0042 y=x/t;
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0043 accept=(((w*(m+y-m*y))<=1) | (w<=(y^(m-1))));
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0044 <span class="keyword">end</span>
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0045 <span class="keyword">end</span>
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0046 gb(i1,i2)=x;
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0047 <span class="keyword">end</span>
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0048 <span class="keyword">end</span>
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0049 <span class="keyword">else</span>
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0050 <span class="comment">% Use Best's rejection algorithm XG, p. 410</span>
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0051 b=m-1;
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0052 c=3*m-0.75;
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0053 <span class="keyword">for</span> i1=1:nrow
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0054 <span class="keyword">for</span> i2=1:ncol
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0055 accept=0;
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0056 <span class="keyword">while</span> accept==0
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0057 u=rand; v=rand;
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0058 w=u*(1-u); y=sqrt(c/w)*(u-0.5);
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0059 x=b+y;
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0060 <span class="keyword">if</span> x >= 0
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0061 z=64*(w^3)*v*v;
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0062 accept=(z<=(1-2*y*y/x)) <span class="keyword">...</span>
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0063 | (log(z)<=(2*(b*log(x/b)-y)));
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0064 <span class="keyword">end</span>
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0065 <span class="keyword">end</span>
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0066 gb(i1,i2)=x;
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0067 <span class="keyword">end</span>
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0068 <span class="keyword">end</span>
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0069 <span class="keyword">end</span>
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0070 gb=gb/k;
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0071
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0072</pre></div>
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<hr><address>Generated on Fri 16-Jun-2006 09:09:06 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/">m2html</a></strong> © 2003</address>
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