The function may be called by the names: g05tjc, nag_rand_int_poisson or nag_rand_poisson.
g05tjc generates integers from a discrete Poisson distribution with mean , 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 g05tjc with the same parameter values can then use this reference vector to generate further variates. The reference array is found using a recurrence relation if is less than and by Stirling's formula otherwise.
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 g05tjc.
Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin
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 g05tjc.
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: – doubleInput
On entry: , the mean of the Poisson distribution.
4: – doubleCommunication Array
On entry: if , the reference vector from the previous call to g05tjc.
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
7: – IntegerOutput
On exit: the pseudorandom numbers from the specified Poisson distribution.
8: – 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, .
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.
lambda is not the same as when r was set up in a previous call.
Previous value of and .
lambda is such that lr would have to be larger than the largest representable integer. Use instead. .
On entry, .
On entry, some of the elements of the array r have been corrupted or have not been initialized.
8Parallelism and Performance
g05tjc 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.
This example prints pseudorandom integers from a Poisson distribution with mean , generated by a single call to g05tjc, after initialization by g05kfc.