heartann 发表于 2009-6-9 18:54
请教高人有SAS random generate的一组服从柯西分布的数~怎样用最大似然数方法估计参数？或者在SAS里做最大似然数估计的方法？谢谢了，我会给认真回答的同学转论坛币的~~~

bobguy 发表于 2010-1-5 11:36

heartann 发表于 2009-6-9 18:54
请教高人有SAS random generate的一组服从柯西分布的数~怎样用最大似然数方法估计参数？或者在SAS里做最大似然数估计的方法？谢谢了，我会给认真回答的同学转论坛币的~~~

There are many prcedures do the ML estimation in SAS. I usually prefer to use NLMIXED and NLP. Actually any SAS procedure has an optimizer(solver) can do ML estimation.

Here are a couple of examples doing CAUCHY distributions( any distribution).

Note: Cauchy distribution has very heavy tail and no moments exist so the GMM and GLS will fail.

data t1;
   alpha2=6.9; beta2=2; seed=(88882);
   do i=1 to 5000;
     x=alpha2+beta2*rancau(seed);
         output;
   end;
run;


proc nlp data=t1;
  max logf;
  parms alpha=1.1, beta=1;
  bounds  beta>0;
  f=1/(beta*3.14159278*(1+((x-alpha)/beta)**2));
  logf=log(f);
run;

proc nlmixed data=t1;
  parms alpha=1.1 beta=1;
  bounds  beta>0;
  f=1/(beta*3.14159278*(1+((x-alpha)/beta)**2));
  logf=log(f);
  model x ~ general(logf);
run;