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SJ1991
Calcite | Level 5

I wanted to understand the math behind the caluclation of Parameter Estimates in the following code. I wnat ot undertsand how the values of theta, scale and shape are computed in SAS, when we equate them to "est". It would be great if anyone could help me understand this. 

 

Code:

 

data Plates;
label Gap = 'Plate Gap in cm';
input Gap @@;
datalines;
-0.746 0.357 0.376 0.327 0.485 1.741 0.241 0.777 0.768 0.409
0.252 0.512 0.534 1.656 0.742 0.378 0.714 1.121 0.597 0.231
0.541 0.805 0.682 0.418 0.506 0.501 0.247 0.922 0.880 0.344
0.519 1.302 0.275 0.601 0.388 0.450 0.845 0.319 0.486 0.529
1.547 0.690 0.676 0.314 0.736 0.643 0.483 0.352 0.636 1.080
;


title 'Distribution of Plate Gaps';
ods output ParameterEstimates GoodnessOfFit FitQuantiles MyHist;
proc univariate data=Plates;
var Gap;
histogram / midpoints=0.2 to 1.8 by 0.2
lognormal(theta=est sigma=est zeta=est)
weibull (theta=est sigma=est c=est)
gamma (theta=est sigma=est alpha=est)
normal
vaxis = axis1
name = 'MyHist';
inset n mean(5.3) std='Std Dev'(5.3) skewness(5.3)
/ pos = ne header = 'Summary Statistics';
axis1 label=(a=90 r=0);

 

Thanks
run;

4 REPLIES 4
SJ1991
Calcite | Level 5
Than You!

I have gone through this document, and understand that theta=est means maximum likelihood estimate of theta. But it would of great help if you can help me understand how this value of theta is calculated.

Let me know if you can help me with this.
PGStats
Opal | Level 21

You can find plenty of good explanations (much better than I could provide, even if I had the time Smiley Happy) by googling "maximum likelihood estimation".

 

There is also the excellent book Continuous Univariate Distributions by Balakrishnan, Johnson, and Kotz

PG
SJ1991
Calcite | Level 5
Thank You!

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