PERT-sampling of data

[user24feb]

I hope this question is admissible as it is not about SAS-syntax, but about the meaning of Rick_SAS's & Ksharp's line of code? The ifn-part, of course, is clear, I am looking for a substantial interpretation or a source of this formula:

_RATE_= ifn((prob<=&peak),prob,2*&peak-prob)

The complete program was:

%let peak=0.7;
title 'Simulation from Normal';
data normal;
call streaminit(1234);
do i=1 to 100000;
 x=rand('normal');
 prob = cdf("Normal", x);
 _RATE_= ifn((prob<=&peak),prob,2*&peak-prob); * <-- distribution function of PERT?? ;
 output;
end;
drop prob ;
run;

proc surveyselect data=normal  out=want method=PPS_WR N=10000;
size _RATE_;    /* specify the probability variable */
run;
proc sgplot data=want;
histogram x;
density x/type=kernel;
run;

The original post was:

https://communities.sas.com/t5/SAS-Statistical-Procedures/Change-statistical-moments-parameters-of-a...

Thanks&kind regards

[Rick_SAS · Accepted solution]

Xia wrote that, so you'll have to ask him what he was thinking.  It looks like he was trying to specify the density for the triangular distribution on [0,1] with peak at &peak. However, the formula he gave is incorrect since it can become negative and doesn't integrate to 1.

If you want the density of the triangular distribution, use the following:

data Triangle;
do x = 0 to 1 by 0.01;
   pdf = ifn((x<=&peak), 2*x/&peak, 2*(1-x)/(1-&peak));
   output;
end;
run;

/* visualize distribution: should have peak at &peak */
proc sgplot data=Triangle;
series x=x y=pdf;
run;

[Ksharp]

Yes. My function is not right only suited for peak=0.5 . What I am trying to do is this . And need new function to compute the sample prob of a value from Normal.

[Ksharp]

Rick's formula is right . Try this one .

%let peak=0.7;
title 'Simulation from Normal';
data normal;
call streaminit(1234);
do i=1 to 100000;
 x=rand('normal');
 prob = cdf("Normal", x);
 if prob=&peak then _RATE_=2;
  else _RATE_= ifn((prob<&peak), 2*prob/&peak, 2*(1-prob)/(1-&peak)); * <-- special sample prob for a value from normal;
 output;
end;
drop prob ;
run;
proc surveyselect data=normal  out=want method=PPS_WR N=10000;
size _RATE_;    /* specify the probability variable */
run;
proc sgplot data=want;
histogram x;
density x/type=kernel;
run;

Edited