NAG Library Routine Document
G05TDF generates a vector of pseudorandom integers from a discrete distribution with a given PDF (probability density function) or CDF (cumulative distribution function) .
|SUBROUTINE G05TDF (
||MODE, N, P, NP, IP1, ITYPE, R, LR, STATE, X, IFAIL)
||MODE, N, NP, IP1, ITYPE, LR, STATE(*), X(N), IFAIL
G05TDF generates a sequence of
, from a discrete distribution defined by information supplied in P
. This may either be the PDF or CDF of the distribution. A reference vector is first set up to contain the CDF of the distribution in its higher elements, followed by an index.
Setting up the reference vector and subsequent generation of variates can each be performed by separate calls to G05TDF or may be combined in a single call.
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 G05TDF.
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 G05TDF.
- 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: P(NP) – REAL (KIND=nag_wp) arrayInput
On entry: the PDF or CDF of the distribution.
- , for ;
- if , ;
- if , .
- 4: NP – INTEGERInput
: the number of values supplied in P
defining the PDF or CDF of the discrete distribution.
- 5: IP1 – INTEGERInput
On entry: the value of the variate, a whole number, to which the probability in corresponds.
- 6: ITYPE – INTEGERInput
: indicates the type of information contained in P
- P contains a probability distribution function (PDF).
- P contains a cumulative distribution function (CDF).
- 7: R(LR) – REAL (KIND=nag_wp) arrayCommunication Array
On entry: if , the reference vector from the previous call to G05TDF.
On exit: the reference vector.
- 8: LR – INTEGERInput
: the dimension of the array R
as declared in the (sub)program from which G05TDF is called.
- if , approximately (for optimum efficiency in generating variates);
- otherwise .
- if or , ;
- if , LR should remain unchanged from the previous call to G05TDF.
- 9: 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.
- 10: X(N) – INTEGER arrayOutput
On exit: contains pseudorandom numbers from the specified discrete distribution.
- 11: 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, .
With , for at least one value of .
With , the sum of , for , does not equal .
With , the values of are not all in non-descending order.
On entry, .
On entry, or .
The value of NP
is not the same as when R
was set up in a previous call to G05TDF 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 variates from a discrete distribution whose PDF,
, is defined as follows:
The reference vector is set up and and the variates are generated by a single call to G05TDF, after initialization by G05KFF
9.1 Program Text
Program Text (g05tdfe.f90)
9.2 Program Data
Program Data (g05tdfe.d)
9.3 Program Results
Program Results (g05tdfe.r)