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Posted 10-23-2018 09:22 PM
(868 views)

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

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

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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

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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.

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

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