Understand the Calculation of Parameter Estimates

[SJ1991]

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;

[lvm]

The User's Guide (avaiable on line) should explain how parameters are estimated in UNIVARIATE for the different distributions. In general, moment estimates are used.

[Rick_SAS]

I disagree with lvm. In general UNIVARIATE uses maximum likelihood estimation.

Moments are used for Normal. Percentile fitting (optionally, moments) are used for the bounded and unbounded Johnson distribution. I believe the remining use MLE.

[lvm]

RIck is right, of course. I was thinking of something else.

[SJ1991]

Thanks Rick.
I understand that these are defined using MLE.
Is there any guide that can help me understand how these values are calculated (step wise calculation of these statements)?

It would be of great help.

[Rick_SAS]

The MLE estimates are obtained by nonlinear optimization of a likelihood or log-likelihood function. For an example, with step-by-step details, see the article "Maximum likelihood estimation in SAS/IML."

[SJ1991]

Thank you Rick!