1: $n$ – Integer Input: On entry: the parameter $n$ of the binomial distribution.

Constraint: $n \geq 0$ .
2: $p$ – Real (Kind=nag_wp) Input: On entry: the parameter $p$ of the binomial distribution.

Constraint: $0.0 < p < 1.0$ .
3: $k$ – Integer Input: On entry: the integer $k$ which defines the required probabilities.

Constraint: $0 \leq k \leq n$ .
4: $plek$ – Real (Kind=nag_wp) Output: On exit: the lower tail probability, $Prob {X \leq k}$ .
5: $pgtk$ – Real (Kind=nag_wp) Output: On exit: the upper tail probability, $Prob {X > k}$ .
6: $peqk$ – Real (Kind=nag_wp) Output: On exit: the point probability, $Prob {X = k}$ .
7: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $- 1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $- 1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $- 1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. 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:

$ifail = 2$: On entry, $p = ⟨ value ⟩$ .
Constraint: $p < 1.0$ .

On entry, $p = ⟨ value ⟩$ .
Constraint: $p > 0.0$ .

$ifail = 3$: On entry, $k = ⟨ value ⟩$ .
Constraint: $k \geq 0$ .

On entry, $k = ⟨ value ⟩$ and $n = ⟨ value ⟩$ .
Constraint: $k \leq n$ .

$ifail = 4$: On entry, n is too large to be represented exactly as a double precision number.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 999$: Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.

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).

g01bjf is not threaded in any implementation.

The time taken by g01bjf 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.

This example reads values of

n

and

p

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

g01bj: FL CL CPP AD