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Posted 12-09-2015 02:45 AM
(852 views)

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;

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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.

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.

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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

PG

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