Hi,
The Proc Severity procedure allows fitting of a 'Burr' distribution but the CDF function does not allow the 'Burr' distribution as an input. For instance I tried this code but does not work:
Cum_Pct_Burr = CDF("Burr", Y, theta,alpha,gamma);
Is there a way to generate a cdf for Burr distribution?
thanks,
A
Hi @aaaaawe2,
Yes, you can use PROC FCMP. And it's relatively easy in this case thanks to the closed-form expression of the Burr distribution's CDF (found in the PROC SEVERITY documentation😞
proc fcmp outlib=work.funcs.prob;
function cdf_burr(x,t,a,g);
return(if x>0 then 1-(1+(x/t)**g)**-a else 0);
endsub;
run;
options cmplib=work.funcs;
For example, plot the CDF for seven parameter combinations (first six also shown in Wikipedia😞
%let n=7;
data burr(rename=(i=start));
array l[&n] _temporary_ (1 1 1 1 1 1 3);
array c[&n] _temporary_ (1 1 1 2 3 0.5 1);
array k[&n] _temporary_ (1 2 3 1 1 2 1);
do x=0 to 5 by 0.01;
do i=1 to &n;
F=cdf_burr(x,l[i],k[i],c[i]);
output;
end;
end;
F=.;
fmtname='legndf';
length label $40;
do i=1 to &n;
label=cats('theta=',l[i],', alpha=', k[i],', gamma=', c[i]);
output;
end;
run;
proc format cntlin=burr(firstobs=3508);
run;
ods graphics on / attrpriority=color;
title 'CDF of Burr distributions';
proc sgplot data=burr;
format start legndf.;
label start='Parameters';
yaxis label='CDF';
series x=x y=F / group=start;
keylegend / location=inside position=bottomright;
run;
title;
Result:
I haven't looked deeper into the related documentation "Defining a Severity Distribution Model with the FCMP Procedure" because I don't have a SAS/ETS license.
@FreelanceReinh SAS/ETS is included in onDemand for Academics if you're ever inclined to try it out.
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