# Samples and permutations

Functions for samples and permutations deliver randomly ordered vectors of data. Random samples may be used for very diverse applications, including simulating rolls of a die, generating anonymised IDs (e.g. for clinical trials), Monte Carlo simulations and wide-range statistical applications.

The following function delivers a vector of longint values, which are randomly ordered and range from min to max:

```type
TLongintvector_data = array of longint;

function sample(min, max: longint; replace: boolean): TLongintvector_data;
var
i, j, num1, num2: longint;
Vector1, Vector2: TLongintvector_data;
begin
randomize;                        // initialise random number generator
num1 := 1 + max - min;            // length of vector to be generated
SetLength(Vector1, num1);         // vector for original (ordered) data
SetLength(Vector2, num1);         // vector with permuted data
if num1 > 0 then
begin
for i := 0 to num1 - 1 do
begin
Vector1[i] := min + i;        // initialise original vector
end;
num2 := num1;
for i := 1 to num1 do
begin
j := random(num2);            // select random element of Vector1
Vector2[i - 1] := Vector1[j]; // and assign to next element of Vector2
if not replace then
begin
Delete(Vector1, j, 1);      // remove randomly selected element
Dec(num2);                  // and adapt size
end;
end;
end;
result := Vector2;
end;
```

Depending on the value of the parameter replace, the random elements of the vector are provided with or without replacement. With replacement, one number may occur several times. Without replacement all elements of the vector will contain unique numbers.