1: $rlamda$ – doubleInput: On entry: the parameter $λ$ of the Poisson distribution.

Constraint: $0.0 < rlamda \leq 10^{6}$ .
2: $k$ – IntegerInput: On entry: the integer $k$ which defines the required probabilities.

Constraint: $k \geq 0$ .
3: $plek$ – double *Output: On exit: the lower tail probability, $Prob \{X \leq k\}$ .
4: $pgtk$ – double *Output: On exit: the upper tail probability, $Prob \{X > k\}$ .
5: $peqk$ – double *Output: On exit: the point probability, $Prob \{X = k\}$ .
6: $fail$ – NagError *Input/Output: The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT_ARG_LT: On entry, $k = 〈value〉$ .
Constraint: $k \geq 0$ .
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
NE_REAL_ARG_GT: On entry, $rlamda = 〈value〉$ .
Constraint: $rlamda \leq 10^{6}$ .
NE_REAL_ARG_LE: On entry, $rlamda = 〈value〉$ .
Constraint: $rlamda > 0.0$ .

7 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).

nag_poisson_dist (g01bkc) is not threaded in any implementation.

The time taken by nag_poisson_dist (g01bkc) depends on

λ

and

k

. For given

λ

, the time is greatest when

k \approx λ

, and is then approximately proportional to

\sqrt{λ}

This example reads values of

λ

and

k

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