NAG Library Function Document

nag_ran_sample_vec (g05ejc)

+− Contents

1 Purpose

nag_ran_sample_vec (g05ejc) selects a pseudorandom sample without replacement from an integer vector.

#include <nag.h>

#include <nagg05.h>

void	nag_ran_sample_vec (const Integer ia[], Integer n, Integer iz[], Integer m, NagError *fail)

nag_ran_sample_vec (g05ejc) performs a single pseudorandom selection of

m

elements from vector ia of length

n

and then places them in vector iz. Their order in ia will be preserved in iz. Each of the

\begin{matrix} n \\ m \end{matrix}

possible combinations of elements of ia may be regarded as being equiprobable.

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

1: ia[n] – const IntegerInput: On entry: the population to be sampled.
2: n – IntegerInput: On entry: the number of elements in the vector to be sampled.
Constraint: $n \geq 1$ .
3: iz[m] – IntegerOutput: On exit: the selected sample.
4: m – IntegerInput: On entry: the sample size.
Constraint: $1 \leq m \leq n$ .
5: fail – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

NE_2_INT_ARG_GT: On entry, $m = 〈value〉$ while $n = 〈value〉$ . These arguments must satisfy $m \leq n$ .
NE_INT_ARG_LT: On entry, $m = 〈value〉$ .
Constraint: $m \geq 1$ .; On entry, $n = 〈value〉$ .
Constraint: $n \geq 1$ .

Not applicable.

n

is greater than 60 it is theoretically impossible to generate all

\begin{matrix} n \\ m \end{matrix}

combinations unless

m

is near 1 or near

n

. This is because the number of possible combinations exceeds the cycle length of the internal random number generator.

The time taken by nag_ran_sample_vec (g05ejc) is of order

n

In order to sample other kinds of objects (i.e., vectors, or matrices of higher dimensions), the following technique may be used:

(a)	Set $ia [i - 1] = i$ , for $i = 1, 2, \dots, n$ (where $n$ is the number of objects)
(b)	Use nag_ran_sample_vec (g05ejc) to take a sample from ia and put it into iz
(c)	Use the contents of iz as a set of indices to access the relevant object.