topic Re: Understand the Calculation of Parameter Estimates in Statistical Procedures

Understand the Calculation of Parameter Estimates

SJ1991 — Wed, 09 Dec 2015 07:42:44 GMT

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;

Re: Understand the Calculation of Parameter Estimates

lvm — Wed, 09 Dec 2015 16:51:54 GMT

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.

Re: Understand the Calculation of Parameter Estimates

Rick_SAS — Wed, 09 Dec 2015 17:44:06 GMT

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.

Re: Understand the Calculation of Parameter Estimates

lvm — Wed, 09 Dec 2015 18:32:17 GMT

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

Re: Understand the Calculation of Parameter Estimates

SJ1991 — Thu, 10 Dec 2015 04:39:48 GMT

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.

Re: Understand the Calculation of Parameter Estimates

Rick_SAS — Thu, 10 Dec 2015 10:18:59 GMT

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."

Re: Understand the Calculation of Parameter Estimates

SJ1991 — Thu, 10 Dec 2015 12:37:46 GMT

Thank you Rick!