I'm tryng to find MLE from inverse gamma distribution using SAS/IML, however when I run optmization appear an error. I suposse the error is because the function 'l' underflow. I have seen the Rick's blog about MLE (http://blogs.sas.com/content/iml/2011/10/12/maximum-likelihood-estimation-in-sasiml.html) and write this code:
proc iml; /*Quantile*/ start qinvgama(p,alpha,beta); qf = 1/quantile("GAMMA",1-p,alpha,beta); return(qf); finish; /*Variate*/ start rinvgama(n,alpha,beta); u = j(n,1); call randgen(u, "Uniform"); rg = qinvgama(u,alpha,beta); return(rg); finish; start MLE(par) global (x); alpha = par[1]; beta = par[2]; n = nrow(x); l = n#(alpha#log(beta) - log(gamma(alpha))) - beta#sum(1/x) - (alpha + 1)#sum(log(x)); return (l); finish; x = rinvgama(100,2,3); sup = { 0 0, . .}; ini = {1.2 3}; opt = {1, 4}; call nlpnra(it, resmle, "MLE", ini, opt, sup); print resmle; quit;
ERROR: (execution) Invalid argument to function.
I think the error message is telling you that the parameters need to be strictly positive. Try
sup = { 1e-8 1e-8,
. .};
Also, there is an easier way to generate from the inverse gamma:
If X ~ gamma(a, b) then 1/X ~ inverse-gamma(a, 1/b)
Some other facts about the inverse gamma distribution is available in the MCMC documentation:
- Definition (search for igamma)
I think the error message is telling you that the parameters need to be strictly positive. Try
sup = { 1e-8 1e-8,
. .};
Also, there is an easier way to generate from the inverse gamma:
If X ~ gamma(a, b) then 1/X ~ inverse-gamma(a, 1/b)
Some other facts about the inverse gamma distribution is available in the MCMC documentation:
- Definition (search for igamma)
Thank you very much Rick. I change the way to generate random variate from the inverse gamma distribution. Now I'm using this:
start rinvgama(n,alpha,beta); aux = j(n,1); call randgen(aux, "Gamma", alpha, 1/beta); rg = 1/aux; return(rg); finish;
While searching my blog for something, I realized that I blogged about how to simulate from the inverse gamma distriution in 2014:
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