topic Understand the calculation of Parameter Estimates in Mathematical Optimization, Discrete-Event Simulation, and OR

Understand the calculation of Parameter Estimates

SJ1991 — Wed, 09 Dec 2015 07:45:04 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

PGStats — Wed, 09 Dec 2015 16:58:59 GMT

Check the documentation at

Formulas for Fitted Continuous Distributions

Re: Understand the calculation of Parameter Estimates

SJ1991 — Thu, 10 Dec 2015 09:35:00 GMT

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.

Re: Understand the calculation of Parameter Estimates

PGStats — Thu, 10 Dec 2015 16:53:05 GMT

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

Re: Understand the calculation of Parameter Estimates

SJ1991 — Fri, 11 Dec 2015 10:20:47 GMT

Thank You!