topic Re: Simulation dataset by given mean, max, min in Statistical Procedures

Simulation dataset by given mean, max, min

Defense — Tue, 31 Jan 2023 18:59:11 GMT

Any one know how to simulate a dataset by given parameters below:

Given parameters: mean=0.195, max=0.26, min=0.13,

Request: random generate a 8 observation dataset with normal distribution.

I try to use rand, but it sounds no option for max and min

data sixnum;
do i=1 to 6;
random=rand("normal", mean, STDDEV );
output;
end;
run;

Thanks

Re: Simulation dataset by given mean, max, min

Defense — Tue, 31 Jan 2023 19:00:35 GMT

My code:
data sixnum;
do i=1 to 8;
random=rand("normal", mean, STDDEV );
output;
end;
run;

Re: Simulation dataset by given mean, max, min

PaigeMiller — Tue, 31 Jan 2023 19:12:25 GMT

@Defense wrote:

Any one know how to simulate a dataset by given parameters below:

Given parameters: mean=0.195, max=0.26, min=0.13,

Request: random generate a 8 observation dataset with normal distribution.

I try to use rand, but it sounds no option for max and min

Do you have any guidance as to what distribution is required here? It can't be normal with a minimum and maximum.

You could cheat and use a normal distribution where the standard deviation is so large that you will virtually never get a value below the min or above the max.

Re: Simulation dataset by given mean, max, min

DanObermiller — Tue, 31 Jan 2023 19:24:35 GMT

@PaigeMiller is correct. A normal distribution can take values from negative infinity to positive infinity. You can get "close" to your maximum and minimum by choosing a standard deviation of the range divided by 6. If you do that, keep in mind that you may still get values above your maximum and/or below your minimum.

Re: Simulation dataset by given mean, max, min

StatDave — Tue, 31 Jan 2023 19:41:48 GMT

The normal distribution only has the mean and standard deviation as parameters. The best you could do would be to choose a standard deviation that will tend to keep the extremes within the min and max that you want. The following uses a sixth of the range as the standard deviation and generates 10,000 observations. Different. seed values in STREAMINIT, different sample sizes, and different proportions of the range will give different results. You'll want to experiment.

data rand;
call streaminit(3525);
mean=.195; std=(.26-.13)/6;
do i=1 to 10000;
random=rand("normal", mean, std );
output;
end;
run;
proc means mean min max std; 
var random; 
run;

Re: Simulation dataset by given mean, max, min

Defense — Tue, 31 Jan 2023 21:33:33 GMT

Thanks for replying. Not sure why using "sixth of the range as the standard deviation".

In addition, I am trying the similar:

data symm(keep=y);
%let

data symm(keep=y);
%let st=0.0012;
seed = 11907665 ;
do i = 1 to 8;
y = rand("Normal", 0.19,&st );

if 0.26>=y>=0.13 then
output;
end;
run;

;

seed = 11907665 ;
do i = 1 to 8;
y = rand("Normal", 0.19,&st );

if 0.26>=y>=0.13 then
output;
end;
run;

I will try st=1/6(max-min), 1/4........1/8 until the output in 0.26>=y>=0.13 that range. Is that make sense

Re: Simulation dataset by given mean, max, min

Reeza — Tue, 31 Jan 2023 21:50:37 GMT

99.9% of data is within plus or minus 3 standard deviations (6 sigma) in a Normal Distribution.

Re: Simulation dataset by given mean, max, min

Defense — Tue, 31 Jan 2023 22:02:43 GMT

Thanks😁😀

Re: Simulation dataset by given mean, max, min

FreelanceReinh — Wed, 01 Feb 2023 10:16:08 GMT

Hello @Defense,

Glad to see that you've got great answers from the experts. Then it would be fair and help later readers if you marked the most helpful reply as the accepted solution, not your own "thank you" post. Could you please change that? It's very easy: Select a different post as the solution after clicking "Not the Solution" in the option menu (see icon below) of the current solution.

Re: Simulation dataset by given mean, max, min

Ksharp — Wed, 01 Feb 2023 11:42:08 GMT

You can calculated P value for MIN and MAX value(take them as percentile).
After that ,sample from PValue_MIN and PValue_MAX , mapping these P value back to percentile.

Check @Rick_SAS 's blog
https://blogs.sas.com/content/iml/2013/07/24/the-truncated-normal-in-sas.html

/*
You can calculated P value for MIN and MAX value(take them as percentile).
After that ,sample from PValue_MIN and PValue_MAX , mapping these P value back to percentile.

Check @Rick_SAS 's blog
https://blogs.sas.com/content/iml/2013/07/24/the-truncated-normal-in-sas.html
*/

%let mean=0.195 ;
%let max=0.26 ;
%let min=0.13 ;
data have;
call streaminit(123);
cdf_min = cdf("Normal", &min., &mean., 0.03);  
cdf_max = cdf("Normal", &max., &mean., 0.03); 
do i=1 to 1000;
  quantile=quantile("Normal", cdf_min + (cdf_max - cdf_min)*rand('uniform'), &mean., 0.03 );
  output;
end;
run;

proc univariate data=have normal;
var quantile;
histogram quantile/normal;
run;

Re: Simulation dataset by given mean, max, min

PaigeMiller — Wed, 01 Feb 2023 11:46:38 GMT

@Defense wrote:

Thanks😁😀

Hello @Defense , you should not mark your own answer, which reads "Thanks" as the correct answer. You need to mark someone else's answer as correct, whichever one you think is correct.

Re: Simulation dataset by given mean, max, min

Defense — Thu, 02 Feb 2023 00:15:30 GMT

This is a great solution. Is 0.03 come from (max-min)/4=S.D?

Re: Simulation dataset by given mean, max, min

Defense — Thu, 02 Feb 2023 00:23:05 GMT

I like to do that. But there are only three icons "Add tag", "Quick reply" and "Reply". No"Not the Solution" icon. Pleae let me know how...Thank

Re: Simulation dataset by given mean, max, min

FreelanceReinh — Thu, 02 Feb 2023 07:53:44 GMT

@Defense wrote:

I like to do that. But there are only three icons "Add tag", "Quick reply" and "Reply". No"Not the Solution" icon. Pleae let me know how...Thank

Click the icon (three horizontal bars) shown in the screenshot in my previous post. This opens the option menu, which should contain the item "Not the Solution" among others.

Re: Simulation dataset by given mean, max, min

Ksharp — Thu, 02 Feb 2023 12:19:22 GMT

Re: Simulation dataset by given mean, max, min

Defense — Thu, 02 Feb 2023 13:27:57 GMT

Thanks

Re: Simulation dataset by given mean, max, min

Rick_SAS — Mon, 20 Feb 2023 13:51:53 GMT

I'm glad you got a response that answers your question. You should select the best response (not your own) as The Solution.

After thinking about this problem, I wrote a short article that shows that you can also solve the problem by using a Beta distribution. The problem does not have a unique solution, so you need to add an additional constraint if you want uniqueness.

See the article, "Simulate from a bounded distribution that has a specified mean."

Re: Simulation dataset by given mean, max, min

sbxkoenk — Mon, 20 Feb 2023 15:22:44 GMT

Simulating data with given (raw) moments, like mean -- variance -- covariance ...
Here's how you can do that !

Creating Synthetic Data with SAS/OR
By Jared Erickson on Operations Research with SAS May 17, 2017
https://blogs.sas.com/content/operations/2017/05/17/creating-synthetic-data-sasor/

Koen

Re: Simulation dataset by given mean, max, min

Rick_SAS — Mon, 20 Feb 2023 15:30:18 GMT

I respectfully disagree. That method (constrained optimization) is not a good way to simulate data.