topic Re: How generate random numbers? in Statistical Procedures

How generate random numbers?

AndersS — Sun, 22 May 2022 15:39:47 GMT

Hi! I want to use a statistical frequency distribution, that is not fully supported by SAS.

I know the exact functional expression.

I can generate random numbers, that are uniformly distributed, using RAND('UNIFORM',0,1).

My question: How can I generate random numbers with this frequency distribution?

/Br Anders

Anders Sköllermo Ph.D., anders.skollermo@one.se

Re: How generate random numbers?

mkeintz — Sun, 22 May 2022 15:50:19 GMT

Do you have a closed form expression for the inverse of the CDF for your distribution? If so, generate a uniform random number for [0,1], and apply the inverse CDF to it.

Re: How generate random numbers?

ballardw — Sun, 22 May 2022 18:02:52 GMT

Can you tell us what distribution or provide a link that defines the distribution?

Hard to provide any significant suggestions without details.

Re: How generate random numbers?

AndersS — Sun, 22 May 2022 19:11:35 GMT

Hi! Many thanks! Yes I will sit down now and try it. /Br Anders

Re: How generate random numbers?

AndersS — Sun, 22 May 2022 20:24:48 GMT

Hi! I tested the GUMBEL distribution. It worked nicely. Below is my SAS-proghram. I think that it is quite OK.
The value of DIFF is zero. Many thanks. /Br Anders

*************************************************************;
*** GUMBEL(0,1) - Quite OK ;

*** GUMBEL(1,2) - Quite OK ;
*************************************************************;

Data work.GUMBEL;
CALL STREAMINIT(2);
do I= 1 to 10;
rvalue = RAND('GUMBEL',1,2);
output;
end;
run;

Data work.MYGUMBEL;
CALL STREAMINIT(2);
do I= 1 to 10;
myunif = RAND('UNIFORM',0,1);
mygumbel = 1 - 2*LOG( -LOG(myunif) );
output;
end;
run;

data work.diff;
merge work.GUMBEL work.MYGUMBEL; by i;
run;

data work.diff;
set work.diff;
diff = rvalue - mygumbel;
output;
run;

Re: How generate random numbers?

Rick_SAS — Mon, 23 May 2022 11:00:27 GMT

This is called the "inverse CDF method" for simulating samples from a formula for the CDF. You can read more about the inverse CDF method and how to implement it in SAS.

If you do not have the formula, you can generate samples from the empirical CDF. If you have the sull ECDF, this is called bootstrapping. If you only have a summary of the CDF (such as published quantiles), you can approximate the ECDF from the quantiles.

Re: How generate random numbers?

AndersS — Mon, 23 May 2022 13:58:11 GMT

VERY GOOD reply by Rick! Many Thanks! / AndersS