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

Constraint: $n \geq 0$ .
2: $p$ – double scalar: The parameter $p$ of the binomial distribution.

Constraint: $0.0 < p < 1.0$ .
3: $k$ – int64int32nag_int scalar: The integer $k$ which defines the required probabilities.

Constraint: $0 \leq k \leq n$ .

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,	$p \leq 0.0$ ,
or	$p \geq 1.0$ .

$ifail = 3$

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

$ifail = 4$

On entry,

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

$ifail = 5$

On entry,

the variance (

= n p (1 - p)

) 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_binomial (g01bj) depends on the variance (

= n p (1 - p)

) and on

k

. For given variance, the time is greatest when

k \approx n p

(

= the mean

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

Example

This example reads values of

n

and

p

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

Open in the MATLAB editor: g01bj_example

function g01bj_example


fprintf('g01bj example results\n\n');

n = int64([4    19     100    2000]);
k = int64([2    13     67     700]);
p =         [0.5  0.44   0.75   0.33];

fprintf('   n     p      k     plek      pgtk      peqk\n');
for i=1:4
  [plek, pgtk, peqk, ifail] = ...
  g01bj(n(i), p(i), k(i));
  fprintf('%5d%7.3f%5d%10.5f%10.5f%10.5f\n', n(i), p(i), k(i), ...
	  plek, pgtk, peqk);
end

g01bj example results

   n     p      k     plek      pgtk      peqk
    4  0.500    2   0.68750   0.31250   0.37500
   19  0.440   13   0.99138   0.00862   0.01939
  100  0.750   67   0.04460   0.95540   0.01700
 2000  0.330  700   0.97251   0.02749   0.00312

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

Chapter Contents

Chapter Introduction

NAG Toolbox