topic Re: How to perform Kolmogorov-Smirnov Test with Weiubll Distribution in SAS in SAS Programming

How to perform Kolmogorov-Smirnov Test with Weiubll Distribution in SAS

Monica_1134 — Thu, 14 Jul 2022 09:39:52 GMT

hi,

I import a excel file in SAS.

The data I need to analyze is called "WD"

I can succeed to perform Weibull distribution for WD.

But I can't find Kolmogorov-Smirnov value on result page.

When I work with Normal and Gumbel Distribution, there is a KS value automatic show on result page.

But if I work with Weibull distribution, there isn't any KS result.

Does anyone know how can I perform this problem?

My programming is:

proc univariate data=a;
histogram WD / weibull;
run;

I also tried this:

proc univariate data=a;
histogram WD / weibull (mu=est sigma=est);
run;

Both of above programming cannot result KS value.

Re: How to perform Kolmogorov-Smirnov Test with Weiubll Distribution in SAS

sbxkoenk — Thu, 14 Jul 2022 10:09:59 GMT

Hello,

The Kolmogorov-Smirnov (KS) goodness-of-fit for the Weibull distribution is NOT given by PROC UNIVARIATE.
Only Cramer-von Mises and Anderson-Darling.

The same is true for SAS/QC PROC CAPABILITY (which can also be used to fit Weibull distribution to observed data).

Maybe you can try SAS/ETS PROC SEVERITY (??).

Why do you absolutely want KS-test?

Thanks,

Koen

Re: How to perform Kolmogorov-Smirnov Test with Weiubll Distribution in SAS

sbxkoenk — Thu, 14 Jul 2022 10:18:19 GMT

Use the inset statement, like :

  inset weibull(shape scale theta ksd ksdpval ad adpval cvm cvmpval)/pos=ne
      header="ABC XYZ";

KSD		Kolmogorov-Smirnov EDF test statistic
KSDPVAL		Kolmogorov-Smirnov EDF test p-value

See :
SAS® 9.4 and SAS® Viya® 3.5 Programming Documentation | SAS 9.4 / Viya 3.5
Base SAS Procedures Guide: Statistical Procedures
The UNIVARIATE Procedure
https://go.documentation.sas.com/doc/en/pgmsascdc/9.4_3.5/procstat/procstat_univariate_syntax15.htm

Koen

Re: How to perform Kolmogorov-Smirnov Test with Weiubll Distribution in SAS

Monica_1134 — Thu, 14 Jul 2022 10:30:14 GMT

hi,

Thank you for your answer!
Actually, I didn't very understand about these statistic distribution methods.
So I don't know it can't apply on it.
The reason why I want to use KS is that I want to compare different distribution plots.

However, how about Chi-square Test?
I tried the same data with following programming:
proc freq data=a;
tables WD / chisq;
run;

The result of this programming is zero. And it also can't apply on assigned distribution method.

I also tried these:
proc capability data=a;
var WD;
histogram / weibull;
run;

proc capabiblity data=a;
var WD;
histogram / gumbel;
run;

There was a result of Chi-square, but the value of it was unreasonable.
The better distribution plot with a larger Chi-square, the worse distribution plot with a smaller Chi-square
.

Re: How to perform Kolmogorov-Smirnov Test with Weiubll Distribution in SAS

sbxkoenk — Thu, 14 Jul 2022 10:49:48 GMT

Hello,

I would not use Chi-Square Goodness of Fit Test for Weibull ,

as the outcome depends on how the continuous values were binned (the midpoints of the histogram bars).

I always use Anderson–Darling test as it is always available !

Cheers,

Koen

Re: How to perform Kolmogorov-Smirnov Test with Weiubll Distribution in SAS

Ksharp — Thu, 14 Jul 2022 12:28:08 GMT

Calling @Rick_SAS

Re: How to perform Kolmogorov-Smirnov Test with Weiubll Distribution in SAS

Rick_SAS — Thu, 14 Jul 2022 13:15:18 GMT

As with all statistical tests, you need to know the null distribution of the test statistic in order to provide p-values. The UNIVARIATE documentation states that the procedure uses results from D’Agostino and Stephens (1986) to estimate the p-values for various combinations of known/unknown parameters. See the table "Availability of EDF Tests" in the doc.

You should use the THETA=, C=, and SIGMA= options to specify the threshold parameter (theta), the shape parameter (c), and the scale parameter (sigma). By default, THETA=0, which means that the default behavior is [theta known, C unknown, Sigma unknown], which is probably why you aren't getting a KS statistic. Try using THETA=EST to get an MLE estimate.