NAG Library Routine Document
G05TJF generates a vector of pseudorandom integers from the discrete Poisson distribution with mean .
||MODE, N, LR, STATE(*), X(N), IFAIL
from a discrete Poisson distribution with mean
, 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 G05TJF 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 routines G05KFF
(for a repeatable sequence if computed sequentially) or G05KGF
(for a non-repeatable sequence) must be called prior to the first call to G05TJF.
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: MODE – INTEGERInput
: a code for selecting the operation to be performed by the routine.
- Set up reference vector only.
- Generate variates using reference vector set up in a prior call to G05TJF.
- Set up reference vector and generate variates.
- Generate variates without using the reference vector.
, , or .
- 2: N – INTEGERInput
On entry: , the number of pseudorandom numbers to be generated.
- 3: LAMBDA – REAL (KIND=nag_wp)Input
On entry: , the mean of the Poisson distribution.
- 4: R(LR) – REAL (KIND=nag_wp) arrayCommunication Array
, the reference vector from the previous call to G05TJF.
is not referenced by G05TJF.
On exit: the reference vector.
- 5: LR – INTEGERInput
: the dimension of the array R
as declared in the (sub)program from which G05TJF is called.
- if , ;
- otherwise .
- if or ,
- if , ;
- otherwise ;
- if , LR must remain unchanged from the previous call to G05TJF.
- 6: STATE() – INTEGER arrayCommunication Array
the actual argument supplied must be the array STATE
supplied to the initialization routines G05KFF
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: X(N) – INTEGER arrayOutput
On exit: the pseudorandom numbers from the specified Poisson distribution.
- 8: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
On entry, , , or .
On entry, .
On entry, .
is such that LR
would have to be larger than the largest representable integer. Use
in this case.
On entry, LAMBDA
is not the same as when R
was set up in a previous call to G05TJF with
On entry, the R
vector was not initialized correctly, or has been corrupted.
On entry, LR
is too small when
|On entry,||STATE vector was not initialized or has been corrupted.|
This example prints
pseudorandom integers from a Poisson distribution with mean
, generated by a single call to G05TJF, after initialization by G05KFF
9.1 Program Text
Program Text (g05tjfe.f90)
9.2 Program Data
Program Data (g05tjfe.d)
9.3 Program Results
Program Results (g05tjfe.r)