Cauchy Distribution Estimation
/*--------------------------------------------------------------
SAS Sample Library
Name: modex12.sas
Description: Example program from SAS/ETS User's Guide,
The MODEL Procedure
Title: Cauchy Distribution Estimation
Product: SAS/ETS Software
Keys: nonlinear simultaneous equation models
PROC: MODEL
Notes:
--------------------------------------------------------------*/
/* Generate a Cauchy distributed Y */
data c;
format date monyy.;
call streaminit(156789);
do t=0 to 20 by 0.1;
date=intnx('month','01jun90'd,(t*10)-1);
x=rand('normal');
e=rand('cauchy') + 10 ;
y=exp(4*x)+e;
output;
end;
run;
title1 'Cauchy Distribution';
proc model data=c ;
dependent y;
parm a -2 nc 4;
y=exp(-a*x);
/* Likelihood function for the residuals */
obj = log(constant('pi')*(1+(-resid.y-nc)**2));
errormodel y ~ general(obj) cdf=cauchy(nc);
fit y / outsn=s1 method=marquardt;
solve y / sdata=s1 data=c(obs=1) random=1000
seed=256789 out=out1;
run;
title 'Distribution of Y';
proc sgplot data=out1;
histogram y;
run;