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

Constraint: $n \geq 0$ .
2: $p$ – double 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: $plek$ – double * Output: On exit: the lower tail probability, $Prob \{X \leq k\}$ .
5: $pgtk$ – double * Output: On exit: the upper tail probability, $Prob \{X > k\}$ .
6: $peqk$ – double * Output: On exit: the point probability, $Prob \{X = k\}$ .
7: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_2_INT_ARG_GT: On entry, $k = 〈value〉$ and $n = 〈value〉$ .
Constraint: $k \leq n$ .
NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_ARG_TOO_LARGE: On entry, n is too large to be represented exactly as a double precision number.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT_ARG_LT: On entry, $k = 〈value〉$ .
Constraint: $k \geq 0$ .

On entry, $n = 〈value〉$ .
Constraint: $n \geq 0$ .
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL_ARG_GE: On entry, $p = 〈value〉$ .
Constraint: $p < 1.0$ .
NE_REAL_ARG_LE: On entry, $p = 〈value〉$ .
Constraint: $p > 0.0$ .
NE_VARIANCE_TOO_LARGE: On entry, the variance $(= n p (1 - p))$ exceeds $10^{6}$ .

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).

g01bjc is not threaded in any implementation.

The time taken by g01bjc 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.

Interfaces: FL CL AD

g01bj: FL CL AD