NAG Library Function Document
nag_prob_hypergeom_vector (g01slc)
1
Purpose
nag_prob_hypergeom_vector (g01slc) returns a number of the lower tail, upper tail and point probabilities for the hypergeometric distribution.
2
Specification
#include <nag.h> |
#include <nagg01.h> |
void |
nag_prob_hypergeom_vector (Integer ln,
const Integer n[],
Integer ll,
const Integer l[],
Integer lm,
const Integer m[],
Integer lk,
const Integer k[],
double plek[],
double pgtk[],
double peqk[],
Integer ivalid[],
NagError *fail) |
|
3
Description
Let
denote a vector of random variables having a hypergeometric distribution with parameters
,
and
. Then
where
,
and
.
The hypergeometric distribution may arise if in a population of size a number are marked. From this population a sample of size is drawn and of these are observed to be marked.
The mean of the distribution , and the variance .
nag_prob_hypergeom_vector (g01slc) computes for given
,
,
and
the probabilities:
,
and
using an algorithm similar to that described in
Knüsel (1986) for the Poisson distribution.
The input arrays to this function are designed to allow maximum flexibility in the supply of vector arguments by re-using elements of any arrays that are shorter than the total number of evaluations required. See
Section 2.6 in the g01 Chapter Introduction for further information.
4
References
Knüsel L (1986) Computation of the chi-square and Poisson distribution SIAM J. Sci. Statist. Comput. 7 1022–1036
5
Arguments
- 1:
– IntegerInput
-
On entry: the length of the array
n.
Constraint:
.
- 2:
– const IntegerInput
-
On entry: , the parameter of the hypergeometric distribution with , , for .
Constraint:
, for .
- 3:
– IntegerInput
-
On entry: the length of the array
l.
Constraint:
.
- 4:
– const IntegerInput
-
On entry: , the parameter of the hypergeometric distribution with , .
Constraint:
.
- 5:
– IntegerInput
-
On entry: the length of the array
m.
Constraint:
.
- 6:
– const IntegerInput
-
On entry: , the parameter of the hypergeometric distribution with , .
Constraint:
.
- 7:
– IntegerInput
-
On entry: the length of the array
k.
Constraint:
.
- 8:
– const IntegerInput
-
On entry: , the integer which defines the required probabilities with , .
Constraint:
.
- 9:
– doubleOutput
-
Note: the dimension,
dim, of the array
plek
must be at least
.
On exit: , the lower tail probabilities.
- 10:
– doubleOutput
-
Note: the dimension,
dim, of the array
pgtk
must be at least
.
On exit: , the upper tail probabilities.
- 11:
– doubleOutput
-
Note: the dimension,
dim, of the array
peqk
must be at least
.
On exit: , the point probabilities.
- 12:
– IntegerOutput
-
Note: the dimension,
dim, of the array
ivalid
must be at least
.
On exit:
indicates any errors with the input arguments, with
- No error.
On entry, | , |
or | , |
or | , |
or | . |
On entry, | is too large to be represented exactly as a real number. |
On entry, | the variance (see Section 3) exceeds . |
- 13:
– 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_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_ARRAY_SIZE
-
On entry, .
Constraint: .
On entry, .
Constraint: .
On entry, .
Constraint: .
On entry, .
Constraint: .
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
- 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.
- NW_IVALID
-
On entry, at least one value of
n,
l,
m or
k was invalid, or the variance was too large.
Check
ivalid for more information.
7
Accuracy
Results are correct to a relative accuracy of at least on machines with a precision of or more decimal digits (provided that the results do not underflow to zero).
8
Parallelism and Performance
nag_prob_hypergeom_vector (g01slc) is not threaded in any implementation.
The time taken by
nag_prob_hypergeom_vector (g01slc) to calculate each probability depends on the variance (see
Section 3) and on
. For given variance, the time is greatest when
(
the mean), and is then approximately proportional to the square-root of the variance.
10
Example
This example reads a vector of values for , , and , and prints the corresponding probabilities.
10.1
Program Text
Program Text (g01slce.c)
10.2
Program Data
Program Data (g01slce.d)
10.3
Program Results
Program Results (g01slce.r)