Hi @Choit and welcome to the SAS Support Communities!
PROC NLIN can estimate the parameters:
data have;
input x y;
cards;
1 0.000516
2 0.000847
3 0.001459
4 0.001939
5 0.002075
6 0.001749
;
ods output ParameterEstimates=est;
proc nlin data=have;
parms a=3 b=2 c=.01;
model y=c*pdf('gamma',x,a,b);
run;
proc print data=est noobs;
var parameter estimate;
run;
Result:
Parameter Estimate a 3.2866 b 2.1503 c 0.0165
The estimates for a and b differ slightly from your Excel values, which might be due to rounding error in variable Y. If the Y values are taken as exact values, the sum of squares is smaller for the above estimates. This is actually not maximum likelihood estimation. The Gauss-Newton method with initial values a=3, b=2, c=.01 was used to minimize the sum of squares.
Hi @Choit and welcome to the SAS Support Communities!
PROC NLIN can estimate the parameters:
data have;
input x y;
cards;
1 0.000516
2 0.000847
3 0.001459
4 0.001939
5 0.002075
6 0.001749
;
ods output ParameterEstimates=est;
proc nlin data=have;
parms a=3 b=2 c=.01;
model y=c*pdf('gamma',x,a,b);
run;
proc print data=est noobs;
var parameter estimate;
run;
Result:
Parameter Estimate a 3.2866 b 2.1503 c 0.0165
The estimates for a and b differ slightly from your Excel values, which might be due to rounding error in variable Y. If the Y values are taken as exact values, the sum of squares is smaller for the above estimates. This is actually not maximum likelihood estimation. The Gauss-Newton method with initial values a=3, b=2, c=.01 was used to minimize the sum of squares.
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