## Proc univariate/severity

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# Proc univariate/severity

I use Proc severity and proc univariate to estimate my parameters of continuous probability function.

I don't understand why statistics of Kolmogorov Smirnov is different with the two proc.

At the same time, statistics have the same definition in the documentation :

http://support.sas.com/documentation/cdl/en/procstat/63104/HTML/default/viewer.htm#procstat_univaria...

http://support.sas.com/documentation/cdl/en/etsug/63348/HTML/default/viewer.htm#etsug_severity_sect0...

Other statistics like Anderson Darling and Cramer-von Mises are the same.

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‎09-06-2016 05:05 AM
SAS Super FREQ
Posts: 3,839

## Re: Proc univariate/severity

I'm away from the office so I can't check D’Agostino, R. and Stephens, M. (1986), Goodness-of-Fit Techniques.

However, my guess is that SEVERITY is using an asymptotic test statistic. Under the null hypothesis, sqrt(N)*D  converges in distribution to another distribution (called the Brownian bridge).  In contrast, UNIVARIATE is probably using table and formulas that describe the distribution of D itself.

For large samples, I would think that the p-values would be similar.

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‎09-06-2016 05:05 AM
SAS Super FREQ
Posts: 3,839

## Re: Proc univariate/severity

I'm away from the office so I can't check D’Agostino, R. and Stephens, M. (1986), Goodness-of-Fit Techniques.

However, my guess is that SEVERITY is using an asymptotic test statistic. Under the null hypothesis, sqrt(N)*D  converges in distribution to another distribution (called the Brownian bridge).  In contrast, UNIVARIATE is probably using table and formulas that describe the distribution of D itself.

For large samples, I would think that the p-values would be similar.

Posts: 5,050

## Re: Proc univariate/severity

You didn't post your code. According to the documentation, the two procedures will be equivalent only when edf=STANDARD is chosen in proc SEVERITY, in the absence of censoring.

PG
SAS Super FREQ
Posts: 3,839

## Re: Proc univariate/severity

To follow up, the main difference seems to be that UNIVARIATE, which does not support censoring, uses one modification of the D statistic, whereas SEVERITY, which does support censoring, uses a slightly different modification.

The PROC SEVERITY formula

D*sqrt(n) + 0.19/sqrt(n))

appears on p. 113 in D'Agostino and Stephens. The formula handles the possibility of censored data and converges to an asymptotic distribution, which is tabulated in Table 4.4 and credited to Koztol and Byar (1975).

Occasional Contributor
Posts: 18

## Re: Proc univariate/severity

Thank you very much
☑ This topic is solved.