## simulating a sample from an empirical distribution

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Super Contributor
Posts: 452

# simulating a sample from an empirical distribution

Hi,

suppose that I have a population of 1000 objects categorized into 3 different types and that 50% of the total objects are Type1, 30% are Type2 and the remaining 20% are Type3.

What I would like to do is to simulate a sample of 100 objects and randomly classify them into 3 types, and the types having the distribution of the population described above.

I found how to simulate samples with embedded distributions, but have difficulty with the empirical distribution.

Thank you!

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Solution
‎05-21-2015 10:45 AM
SAS Super FREQ
Posts: 3,839

## Re: simulating a sample from an empirical distribution

[ Edited ]

This is exactly the example that I use on p. 18-19 of my book Simulating Data with SAS.  The code is

``````%let N = 100;
data Table(keep=x);
call streaminit(4321);
array p[3] _temporary_ (0.5 0.2 0.3);  /* proportions in population */
do i = 1 to &N;
x = rand("Table", of p[*]);           /* sample with replacement */
output;
end;
run;``````

For an explanation and alternatives, see the blog post "Simulate categorical data in SAS."

By the way, the size of the population doesn't matter. Only the proportions.

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Super User
Posts: 11,810

## Re: simulating a sample from an empirical distribution

If you have a category variable then sort by the category variable and:

proc survey select data=have out=want

sampsize=100;

strata category/ alloc=prop;

run;

might work

Occasional Contributor
Posts: 7

## Re: simulating a sample from an empirical distribution

That will give a sample with exactly the same distribution (exactly 50 that are Type 1 etc). If you want to randomly sample, then you also need to know whether you are sampling from a population of size 1000 (without replacement) or from an infinite population.

Briefly, these could be achieved by:

Population size=1000: assign a random number to each observation, sort and take the first 100.

Population size = infinite: generate a set of 100 random numbers between 1 and 1000. Merge this (by a variable containing observation number) with your data set of 1000 keeping those that were in your random number list (may include duplicates, because it is sampling with replacement).

Solution
‎05-21-2015 10:45 AM
SAS Super FREQ
Posts: 3,839

## Re: simulating a sample from an empirical distribution

[ Edited ]

This is exactly the example that I use on p. 18-19 of my book Simulating Data with SAS.  The code is

``````%let N = 100;
data Table(keep=x);
call streaminit(4321);
array p[3] _temporary_ (0.5 0.2 0.3);  /* proportions in population */
do i = 1 to &N;
x = rand("Table", of p[*]);           /* sample with replacement */
output;
end;
run;``````

For an explanation and alternatives, see the blog post "Simulate categorical data in SAS."

By the way, the size of the population doesn't matter. Only the proportions.

Super Contributor
Posts: 452

## Re: simulating a sample from an empirical distribution

omg I actually bought this book last year and even read section 2.4.5 Tabulated Distributions with the socks example (I even highlighted parts of the text)!!!!

Its just that since then I completely forgot about it...

Thanks Rick!!!

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