1: $n$ – int64int32nag_int scalar: The parameter $n$ of the hypergeometric distribution.

Constraint: $n \geq 0$ .
2: $l$ – int64int32nag_int scalar: The parameter $l$ of the hypergeometric distribution.

Constraint: $0 \leq l \leq n$ .
3: $m$ – int64int32nag_int scalar: The parameter $m$ of the hypergeometric distribution.

Constraint: $0 \leq m \leq n$ .
4: $k$ – int64int32nag_int scalar: The integer $k$ which defines the required probabilities.

Constraint: $\max (0, l - (n - m)) \leq k \leq \min (l, m)$ .

Optional Input Parameters

None.

Output Parameters

1: $plek$ – double scalar: The lower tail probability, $Prob \{X \leq k\}$ .
2: $pgtk$ – double scalar: The upper tail probability, $Prob \{X > k\}$ .
3: $peqk$ – double scalar: The point probability, $Prob \{X = k\}$ .
4: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$

On entry,

n < 0

$ifail = 2$

On entry,	$l < 0$ ,
or	$l > n$ .

$ifail = 3$

On entry,	$m < 0$ ,
or	$m > n$ .

$ifail = 4$

On entry,	$k < 0$ ,
or	$k > l$ ,
or	$k > m$ ,
or	$k < l + m - n$ .

$ifail = 5$

On entry,

n is too large to be represented exactly as a double number.

$ifail = 6$

On entry,

the variance (see Description) exceeds

10^{6}

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Results are correct to a relative accuracy of at least

10^{- 6}

on machines with a precision of

9

or more decimal digits, and to a relative accuracy of at least

10^{- 3}

on machines of lower precision (provided that the results do not underflow to zero).

Further Comments

The time taken by nag_stat_prob_hypergeom (g01bl) depends on the variance (see Description) and on

k

. For given variance, the time is greatest when

k \approx l m / n

(

=

the mean), and is then approximately proportional to the square-root of the variance.

Example

This example reads values of

n

l

m

and

k

from a data file until end-of-file is reached, and prints the corresponding probabilities.

Open in the MATLAB editor: g01bl_example

function g01bl_example


fprintf('g01bl example results\n\n');

n = int64([10 40 155 1000]);
l = int64([ 2 10  35  444]);
m = int64([ 5  3 122  500]);
k = int64([ 1  2  22  220]);

fprintf('    n   l   m   k     plek      pgtk      peqk\n');
for i = 1:4
  [plek, pgtk, peqk, ifail] = ...
  g01bl(n(i), l(i), m(i), k(i));

  fprintf('%5d%4d%4d%4d%10.5f%10.5f%10.5f\n', n(i), l(i), m(i), k(i), ...
	  plek, pgtk, peqk);
end

g01bl example results

    n   l   m   k     plek      pgtk      peqk
   10   2   5   1   0.77778   0.22222   0.55556
   40  10   3   2   0.98785   0.01215   0.13664
  155  35 122  22   0.01101   0.98899   0.00779
 1000 444 500 220   0.42429   0.57571   0.04913

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox