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NAG[g05mlc] NAG[nag_rngs_hypergeometric] - Generates a vector of random integers from a hypergeometric distribution, seeds and generator number passed explicitly
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Calling Sequence
g05mlc(mode, ns, np, m, x, igen, iseed, r, 'n'=n, 'fail'=fail)
nag_rngs_hypergeometric(. . .)
Parameters
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mode - integer;
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On entry: a code for selecting the operation to be performed by the function:
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 Set up reference vector only.
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 Generate variates using reference vector set up in a prior call to nag_rngs_hypergeometric (g05mlc).
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 Set up reference vector and generate variates.
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 Generate variates without using the reference vector.
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Constraint:  . .
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ns - integer;
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On entry:  , the sample size of the hypergeometric distribution.
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Constraint:  . .
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np - integer;
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On entry:  , the population size of the hypergeometric distribution.
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Constraint:  . .
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m - integer;
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On entry:  , the number of specified items of the hypergeometric distribution.
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Constraint:  . .
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x - Vector(1..n, datatype=integer[kernelopts('wordsize')/8]);
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On exit: the  pseudo-random numbers from the specified hypergeometric distribution.
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iseed - Vector(1.. , datatype=integer[kernelopts('wordsize')/8]);
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On entry: contains values which define the current state of the selected generator.
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On exit: contains updated values defining the new state of the selected generator.
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r - Vector(1.. , datatype=float[8]);
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Note: the dimension, dim, of the array r must be at least  .
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On entry: if mode is set to  , the reference vector from the previous call to nag_rngs_hypergeometric (g05mlc).
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On exit: the reference vector.
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'n'=n - integer; (optional)
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On entry: the number of pseudo-random numbers to be generated.
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Constraint:  . .
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'fail'=fail - table; (optional)
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The NAG error argument, see the documentation for NagError.
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Description
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Purpose
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nag_rngs_hypergeometric (g05mlc) generates a vector of pseudo-random 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.
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Description
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nag_rngs_hypergeometric (g05mlc) generates  integers ![x[i]](/support/helpjp/helpview.aspx?si=9881/file08516/math183.png) from a discrete hypergeometric distribution, where the probability of ![x[i] = I](/support/helpjp/helpview.aspx?si=9881/file08516/math185.png) is
![[[P(i,=,I)=(l!m!(n,-,l)!(n,-,m)!)/(I!(l,-,I)!(m,-,I)!(n,-,m,-,l,+,I)!n!), I=max(0,,,m+l-n),..,min(l,,,m) ],[],[P(i,=,I)=0, ]]](/support/helpjp/helpview.aspx?si=9881/file08516/math188.png)
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_rngs_hypergeometric (g05mlc) with the same argument 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 g05kbc (nag_rngs_init_repeatable) (for a repeatable sequence if computed sequentially) or g05kcc (nag_rngs_init_nonrepeatable) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_hypergeometric (g05mlc).
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Error Indicators and Warnings
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"NE_BAD_PARAM"
On entry, argument  had an illegal value.
"NE_INT"
On entry,  . Constraint:  .
On entry,  . Constraint:  .
On entry,  . Constraint:  .
"NE_INT_2"
On entry,  or  :  ,  .
On entry,  or  :  ,  .
"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 consult NAG for assistance.
"NE_PREV_CALL"
ns or np or m is not the same as when r was set up in a previous call or the data in r has been corrupted.
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Examples
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mode := 2:
ns := 500:
np := 1000:
m := 900:
n := 20:
igen := 1:
x := Vector(20, datatype=integer[kernelopts('wordsize')/8]):
iseed := Vector([1762543, 9324783, 42344, 742355], datatype=integer[kernelopts('wordsize')/8]):
r := Vector(2519, datatype=float[8]):
# Initialise seeds
NAG:-g05kbc(igen, iseed):
NAG:-g05mlc(mode, ns, np, m, x, igen, iseed, r, 'n' = n):
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