NAG Library Routine Document
G05SEF generates a vector of pseudorandom numbers taken from a Dirichlet distribution.
||N, M, STATE(*), LDX, IFAIL
The distribution has PDF (probability density function)
is a vector of dimension
, such that
G05SEF generates a draw from a Dirichlet distribution by first drawing independent samples, , i.e., independent draws from a gamma distribution with parameters and one, and then setting .
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 G05SEF.
Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth
- 1: N – INTEGERInput
On entry: , the number of pseudorandom numbers to be generated.
- 2: M – INTEGERInput
On entry: , the number of dimensions of the distribution.
- 3: A(M) – REAL (KIND=nag_wp) arrayInput
On entry: the parameter vector for the distribution.
, for .
- 4: 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.
- 5: X(LDX,M) – REAL (KIND=nag_wp) arrayOutput
On exit: the pseudorandom numbers from the specified Dirichlet distribution, with holding the th dimension for the th variate.
- 6: LDX – INTEGERInput
: the first dimension of the array X
as declared in the (sub)program from which G05SEF is called.
- 7: 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, .
On entry, .
On entry, at least one .
|On entry,||STATE vector was not initialized or has been corrupted.|
On entry, .
This example prints a set of five pseudorandom numbers from a Dirichlet distribution with parameters
, generated by a single call to G05SEF, after initialization by G05KFF
9.1 Program Text
Program Text (g05sefe.f90)
9.2 Program Data
Program Data (g05sefe.d)
9.3 Program Results
Program Results (g05sefe.r)