NAG Library Routine Document
G05SRF generates a vector of pseudorandom numbers from a von Mises distribution with concentration parameter .
||N, STATE(*), IFAIL
The von Mises distribution is a symmetric distribution used in the analysis of circular data. The PDF (probability density function) of this distribution on the circle with mean direction
and concentration parameter
, can be written as:
is reduced modulo
. For very small
the distribution is almost the uniform distribution, whereas for
all the probability is concentrated at one point.
, are generated using an envelope rejection method with a wrapped Cauchy target distribution as proposed by Best and Fisher (1979)
and described by Dagpunar (1988)
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 G05SRF.
Best D J and Fisher N I (1979) Efficient simulation of the von Mises distribution Appl. Statist. 28 152–157
Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press
Mardia K V (1972) Statistics of Directional Data Academic Press
- 1: N – INTEGERInput
On entry: , the number of pseudorandom numbers to be generated.
- 2: VK – REAL (KIND=nag_wp)Input
On entry: , the concentration parameter of the required von Mises distribution.
- 3: 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.
- 4: X(N) – REAL (KIND=nag_wp) arrayOutput
On exit: the pseudorandom numbers from the specified von Mises distribution.
- 5: 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,||STATE vector was not initialized or has been corrupted.|
For a given number of random variates the generation time increases slightly with increasing .
This example prints the first five pseudorandom numbers from a von Mises distribution with
, generated by a single call to G05SRF, after initialization by G05KFF
9.1 Program Text
Program Text (g05srfe.f90)
9.2 Program Data
Program Data (g05srfe.d)
9.3 Program Results
Program Results (g05srfe.r)