1. Sampling Distribution of the Mean in IML

2. Complete code for data step version
%let obs = 10;
%let reps = 1000;
data uniforms;
call streaminit(54321);
do rep = 1 to &reps;
do i = 1 to &obs;
x = rand("Uniform");
output;
end;
run;
proc means data=uniforms noprint;
by rep;
var x;
output out=MeansUni mean=Meanx;
proc univariate data=meansuni;
label meanx = "Sample Mean of U(0,1) Data";
histogram Meanx / normal;
ods select Histogram moments;

3. In the IML version, each sample is stored as a row in a matrix and we use the mean function to calculate the sample means.
There are no loops
Three statements: Randseed, J, and Randgen generate the samples. Randgen can fill an entire matrix with random values.

4. %let obs = 10;
%let reps = 1000;
proc iml;
call randseed(123);
x = j(&reps,&obs); /* many samples (rows), each of size N */
call randgen(x, "Uniform"); /* 1. Simulate data */
s = x[,:]; /* 2. Compute statistic for each row */
Mean = mean(s); /* 3. Summarize and analyze ASD */
StdDev = std(s);
call qntl(q, s, { });
print Mean StdDev (q`)[colname={"5th Pctl" "95th Pctl"}];
/* compute proportion of statistics greater than 0.7 */
Prob = mean(s > 0.7);
print Prob[format=percent7.2];
quit;

5. Create a data set in wide format
%let obs = 10;
%let reps = 1000;
proc iml;
call randseed(123);
x = j(&reps,&obs); /* many samples (rows), each of size N */
call randgen(x, "Uniform"); /* 1. Simulate data*/
c="x1":"x&obs";
show c;
create unif from x [colname=c];
append from x;
close unif;
quit;
proc contents data=unif;
run;

6. Summarize data set in wide format
%let obs=10;
data stats (keep=mean std max);
set unif;
mean=mean(of x1-x10);
std=std(of x1-x10);
max=max(of x:);
run;
proc means data=stats;
proc univariate data=stats;
var mean std max;
ods select qqplot;
qqplot mean std max;

7. Restructure data into long format using IML

8. %let obs=3;
%let reps=5;
%let seed=54321;
proc iml;
reset print;
call randseed(54321);
x = j(&reps,&obs);
call randgen(x, "Uniform");
print x;
rep = repeat( T(1:&reps), 1, &obs);
rep = shape(rep, 0, 1);
z = shape(x, 0, 1);
create Long var{rep z}; append; close Long;
create Long2 var{rep x}; append; close Long2;
quit;
proc print data=long(obs=5);run;
proc print data=long2(obs=5);run;

9. /**********************/
/* Answer to exercise 4.8*/
proc iml;
call randseed(123);
x = j(10000, 10);
call randgen(x, "Uniform"); * 1. Simulate data;
s = x[,<>]; * 2. Compute statistic for each row;
Mean = mean(s); * 3. Summarize and analyze ASD;
StdDev = std(s);
call qntl(q, s, { });
print Mean StdDev (q`)[colname={"5th Pctl" "95th Pctl"}];
create MaxDist var {s}; append; close MaxDist;
/*Sampling Normal Means, IML*/
%let N = 31; /* size of each sample */
%let NumSamples = 10000; /* number of samples */
samples=j(&numsamples,&n,.);
call randgen(samples,"Normal");
samplemeans=samples[,:];
create means var {samplemean};
append from samplemeans;
close means;
quit;