NAG Library Routine Document

G01BKF

1: RLAMDA – REAL (KIND=nag_wp)Input: 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 – REAL (KIND=nag_wp)Output: On exit: the lower tail probability, $Prob \{X \leq k\}$ .
4: PGTK – REAL (KIND=nag_wp)Output: On exit: the upper tail probability, $Prob \{X > k\}$ .
5: PEQK – REAL (KIND=nag_wp)Output: On exit: the point probability, $Prob \{X = k\}$ .
6: IFAIL – INTEGERInput/Output: On entry: IFAIL must be set to $0$ , $- 1 or 1$ . If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value $- 1 or 1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is $0$ . When the value $- 1 or 1$ is used it is essential to test the value of IFAIL on exit.

On exit: $IFAIL = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

IFAIL = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by X04AAF).

Errors or warnings detected by the routine:

$IFAIL = 1$

On entry,

RLAMDA \leq 0.0

$IFAIL = 2$

On entry,

K < 0

$IFAIL = 3$

On entry,

RLAMDA > 10^{6}

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).

The time taken by G01BKF 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.