1: $rlamda$ – double scalar: The parameter $λ$ of the Poisson distribution.

Constraint: $0.0 < rlamda \leq 10^{6}$ .
2: $k$ – int64int32nag_int scalar: The integer $k$ which defines the required probabilities.

Constraint: $k \geq 0$ .

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,

rlamda \leq 0.0

$ifail = 2$

On entry,

k < 0

$ifail = 3$

On entry,

rlamda > 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_poisson (g01bk) depends on

λ

and

k

. For given

λ

, the time is greatest when

k \approx λ

, and is then approximately proportional to

\sqrt{λ}

Example

This example reads values of

λ

and

k

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

Open in the MATLAB editor: g01bk_example

function g01bk_example


fprintf('g01bk example results\n\n');

rlamda =    [0.75  9.2  34  175];
k = int64([3     12   25  175]);

fprintf('  rlamda     k     plek      pgtk      peqk\n');
for i=1:4
  [plek, pgtk, peqk, ifail] = ...
  g01bk(rlamda(i), k(i));

  fprintf('%8.3f%6d%10.5f%10.5f%10.5f\n', rlamda(i), k(i), plek, pgtk, peqk);
end

g01bk example results

  rlamda     k     plek      pgtk      peqk
   0.750     3   0.99271   0.00729   0.03321
   9.200    12   0.86074   0.13926   0.07755
  34.000    25   0.06736   0.93264   0.02140
 175.000   175   0.52009   0.47991   0.03014

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

Chapter Contents

Chapter Introduction

NAG Toolbox