NAG Library Function Document
nag_rand_hypergeometric (g05tec) generates a vector of pseudorandom integers from the discrete hypergeometric distribution of the number of specified items in a sample of size , taken from a population of size with specified items in it.
||nag_rand_hypergeometric (Nag_ModeRNG mode,
nag_rand_hypergeometric (g05tec) generates
from a discrete hypergeometric distribution, where the probability of
The variates can be generated with or without using a search table and index. If a search table is used then it is stored with the index in a reference vector and subsequent calls to nag_rand_hypergeometric (g05tec) with the same parameter values can then use this reference vector to generate further variates. The reference array is generated by a recurrence relation if , otherwise Stirling's approximation is used.
One of the initialization functions nag_rand_init_repeatable (g05kfc)
(for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc)
(for a non-repeatable sequence) must be called prior to the first call to nag_rand_hypergeometric (g05tec).
Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley
mode – Nag_ModeRNGInput
: a code for selecting the operation to be performed by the function.
- Set up reference vector only.
- Generate variates using reference vector set up in a prior call to nag_rand_hypergeometric (g05tec).
- Set up reference vector and generate variates.
- Generate variates without using the reference vector.
, , or .
n – IntegerInput
On entry: , the number of pseudorandom numbers to be generated.
ns – IntegerInput
On entry: , the sample size of the hypergeometric distribution.
np – IntegerInput
On entry: , the population size of the hypergeometric distribution.
m – IntegerInput
On entry: , the number of specified items of the hypergeometric distribution.
r[lr] – doubleCommunication Array
, the reference vector from the previous call to nag_rand_hypergeometric (g05tec).
is not referenced by nag_rand_hypergeometric (g05tec).
On exit: the reference vector.
lr – IntegerInput
: the dimension of the array r
- if , approximately;
- otherwise .
- if or , lr must not be too small, but the limit is too complicated to specify;
- if , lr must remain unchanged from the previous call to nag_rand_hypergeometric (g05tec).
state – IntegerCommunication Array
the actual argument supplied must be the array state
supplied to the initialization functions nag_rand_init_repeatable (g05kfc)
or nag_rand_init_nonrepeatable (g05kgc)
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
x[n] – IntegerOutput
On exit: the pseudorandom numbers from the specified hypergeometric distribution.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, argument had an illegal value.
On entry, lr
is too small when
, minimum length required
On entry, .
On entry, .
On entry, and .
On entry, and .
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
On entry, state
vector has been corrupted or not initialized.
The value of ns
is not the same as when r
was set up
in a previous call with
On entry, some of the elements of the array r
have been corrupted or have not been initialized.
The example program prints
pseudorandom integers from a hypergeometric distribution with
, generated by a single call to nag_rand_hypergeometric (g05tec), after initialization by nag_rand_init_repeatable (g05kfc)
9.1 Program Text
Program Text (g05tece.c)
9.2 Program Data
9.3 Program Results
Program Results (g05tece.r)