## Fitting a gamma curve and mle?

Hi,
Trying to find a way in SAS to solve relationshio between x and y which have a gamma curve relationship,
Data as below

X Y
1 0.000516
2 0.000847
3 0.001459
4 0.001939
5 0.002075
6 0.001749

Relationship solved using excel using minimum error square
Y=gamma.dist(x,3.2840,2.1535,0) * 0.0165

How do i get sas to solve to the parameter as how excel does to get the 3 parameters in the function above
3.2840 , 2.1535 , 0.0165

Thanks

1 ACCEPTED SOLUTION

Accepted Solutions

## Re: Fitting a gamma curve and mle?

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.

2 REPLIES 2

## Re: Fitting a gamma curve and mle?

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.

## Re: Fitting a gamma curve and mle?

For more on using PROC NLIN to fit nonlinear curves, see the article

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