NAG Library Routine Document
G05TAF generates a vector of pseudorandom integers from the discrete binomial distribution with parameters and .
||MODE, N, M, LR, STATE(*), X(N), IFAIL
from a discrete binomial distribution, where the probability of
. This represents the probability of achieving
trials when the probability of success at a single trial 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 G05TAF with the same parameter values can then use this reference vector to generate further variates.
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 G05TAF.
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 G05TAF.
- 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: M – INTEGERInput
On entry: , the number of trials of the distribution.
- 4: P – REAL (KIND=nag_wp)Input
On entry: , the probability of success of the binomial distribution.
- 5: R(LR) – REAL (KIND=nag_wp) arrayCommunication Array
, the reference vector from the previous call to G05TAF.
is not referenced by G05TAF.
On exit: the reference vector.
- 6: LR – INTEGERInput
: the dimension of the array R
as declared in the (sub)program from which G05TAF is called.
- if , ;
- otherwise .
- if or ,
- if , LR must remain unchanged from the previous call to G05TAF.
- 7: 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.
- 8: X(N) – INTEGER arrayOutput
On exit: the pseudorandom numbers from the specified binomial distribution.
- 9: 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, .
On entry, M
is not the same as when R
was set up in a previous call to G05TAF 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 binomial distribution with parameters
, generated by a single call to G05TAF, after initialization by G05KFF
9.1 Program Text
Program Text (g05tafe.f90)
9.2 Program Data
Program Data (g05tafe.d)
9.3 Program Results
Program Results (g05tafe.r)