NAG Library Function Document

nag_hypergeom_dist (g01blc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{n}$ – IntegerInput

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

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

2:    $\mathbf{l}$ – IntegerInput

On entry: the parameter $l$ of the hypergeometric distribution.

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

3:    $\mathbf{m}$ – IntegerInput

On entry: the parameter $m$ of the hypergeometric distribution.

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

4:    $\mathbf{k}$ – IntegerInput

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

Constraint: $\max \left(0,\mathbf{l}-\left(\mathbf{n}-\mathbf{m}\right)\right)\le \mathbf{k}\le \min \left(\mathbf{l},\mathbf{m}\right)$.

5:    $\mathbf{plek}$ – double *Output

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

6:    $\mathbf{pgtk}$ – double *Output

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

7:    $\mathbf{peqk}$ – double *Output

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

8:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

NE_2_INT_ARG_GT

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

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

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

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

NE_4_INT_ARG_CONS

On entry, $\mathbf{k}=〈\mathit{\text{value}}〉$, $\mathbf{l}=〈\mathit{\text{value}}〉$, $\mathbf{m}=〈\mathit{\text{value}}〉$ and $\mathbf{l}+\mathbf{m}-\mathbf{n}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{k}\ge \mathbf{l}+\mathbf{m}-\mathbf{n}$.

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_ARG_TOO_LARGE

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

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ had an illegal value.

NE_INT_ARG_LT

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

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

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

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

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 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_VARIANCE_TOO_LARGE

On entry, the variance $=\frac{lm\left(n-l\right)\left(n-m\right)}{n^2\left(n-1\right)}$ exceeds ${10}^6$.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01blce.c)

10.2

Program Data

Program Data (g01blce.d)

10.3

Program Results

Program Results (g01blce.r)