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;
You can find plenty of good explanations (much better than I could provide, even if I had the time ) by googling "maximum likelihood estimation".
There is also the excellent book Continuous Univariate Distributions by Balakrishnan, Johnson, and Kotz
Don't miss out on SAS Innovate - Register now for the FREE Livestream!
Can't make it to Vegas? No problem! Watch our general sessions LIVE or on-demand starting April 17th. Hear from SAS execs, best-selling author Adam Grant, Hot Ones host Sean Evans, top tech journalist Kara Swisher, AI expert Cassie Kozyrkov, and the mind-blowing dance crew iLuminate! Plus, get access to over 20 breakout sessions.
Learn how to run multiple linear regression models with and without interactions, presented by SAS user Alex Chaplin.
Find more tutorials on the SAS Users YouTube channel.