RNVMS

Generates pseudorandom numbers from a von Mises distribution.

Required Arguments

C — Parameter of the von Mises distribution. (Input)
This parameter must be greater than one half of machine epsilon. (On many machines, the lower bound for C is 10‑3.)

R — Vector of length NR containing the random von Mises deviates. (Output)

Optional Arguments

NR — Number of random numbers to generate. (Input)
Default: NR = size (R,1).

FORTRAN 90 Interface

Generic: CALL RNVMS (C, R [, …])

Specific: The specific interface names are S_RNVMS and D_RNVMS.

FORTRAN 77 Interface

Single: CALL RNVMS (NR, C, R)

Double: The double precision name is DRNVMS.

Description

Routine RNVMS generates pseudorandom numbers from a von Mises distribution with parameter C, which must be positive. With c = C, the probability density function is

 

where I0(c) is the modified Bessel function of the first kind of order 0. The probability density equals 0 outside the interval (–π, π).

The algorithm is an acceptance/rejection method using a wrapped Cauchy distribution as the majorizing distribution. It is due to Best and Fisher (1979).

Comments

The routine RNSET can be used to initialize the seed of the random number generator. The routine RNOPT can be used to select the form of the generator.

Example

In this example, RNVMS is used to generate five pseudorandom von Mises variates with c = 1.

 

USE RNVMS_INT

USE UMACH_INT

USE RNSET_INT

 

IMPLICIT NONE

INTEGER NR

PARAMETER (NR=5)

!

INTEGER ISEED, NOUT

REAL C, R(NR)

!

CALL UMACH (2, NOUT)

C = 1.0

ISEED = 123457

CALL RNSET (ISEED)

CALL RNVMS (C, R)

WRITE (NOUT,99999) R

99999 FORMAT (' Von Mises random deviates: ', 5F8.4)

END

Output

 

Von Mises random deviates: 0.2472 -2.4326 -1.0216 -2.1722 -0.5029