NAG FL Interface
g01bjf (prob_​binomial)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{n}$ – Integer Input

On entry: the parameter $n$ of the binomial distribution.

Constraint: $\mathbf{n}\ge 0$.

2: $\mathbf{p}$ – Real (Kind=nag_wp) Input

On entry: the parameter $p$ of the binomial distribution.

Constraint: $0.0<\mathbf{p}<1.0$.

3: $\mathbf{k}$ – Integer Input

On entry: the integer $k$ which defines the required probabilities.

Constraint: $0\le \mathbf{k}\le \mathbf{n}$.

4: $\mathbf{plek}$ – Real (Kind=nag_wp) Output

On exit: the lower tail probability, $\mathrm{Prob}\left\{X\le k\right\}$.

5: $\mathbf{pgtk}$ – Real (Kind=nag_wp) Output

On exit: the upper tail probability, $\mathrm{Prob}\left\{X>k\right\}$.

6: $\mathbf{peqk}$ – Real (Kind=nag_wp) Output

On exit: the point probability, $\mathrm{Prob}\left\{X=k\right\}$.

7: $\mathbf{ifail}$ – 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 $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.

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

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{n}\ge 0$.

$\mathbf{ifail}=2$

On entry, $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{p}<1.0$.

On entry, $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{p}>0.0$.

$\mathbf{ifail}=3$

On entry, $\mathbf{k}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{k}\ge 0$.

On entry, $\mathbf{k}=〈\mathit{\text{value}}〉$ and $\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{k}\le \mathbf{n}$.

$\mathbf{ifail}=4$

On entry, n is too large to be represented exactly as a double precision number.

$\mathbf{ifail}=5$

On entry, the variance $\left(=np\left(1-p\right)\right)$ exceeds ${10}^6$.

$\mathbf{ifail}=-99$

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.

$\mathbf{ifail}=-399$

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.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results