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.
The function may be called by the names: g05tec, nag_rand_int_hypergeom or nag_rand_hypergeometric.
g05tec generates integers from a discrete hypergeometric distribution, where the probability of is
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 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 g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to g05tec.
Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley
1: – Nag_ModeRNGInput
On entry: 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 g05tec.
Set up reference vector and generate variates.
Generate variates without using the reference vector.
, , or .
2: – IntegerInput
On entry: , the number of pseudorandom numbers to be generated.
3: – IntegerInput
On entry: , the sample size of the hypergeometric distribution.
4: – IntegerInput
On entry: , the population size of the hypergeometric distribution.
5: – IntegerInput
On entry: , the number of specified items of the hypergeometric distribution.
6: – doubleCommunication Array
On entry: if , the reference vector from the previous call to g05tec.
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
9: – IntegerOutput
On exit: the pseudorandom numbers from the specified hypergeometric distribution.
10: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, lr is too small when or : , 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 for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
On entry, state vector has been corrupted or not initialized.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
The value of ns, np or m is not the same as when r was set up in a previous call with or .
On entry, some of the elements of the array r have been corrupted or have not been initialized.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
g05tec is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.
The example program prints pseudorandom integers from a hypergeometric distribution with , and , generated by a single call to g05tec, after initialization by g05kfc.