randomVonMises¶

Generates pseudorandom numbers from a von Mises distribution.

Synopsis¶

randomVonMises (nRandom, c)

Required Arguments¶

int nRandom (Input): Number of random numbers to generate.
float c (Input): Parameter of the von Mises distribution. This parameter must be greater than one-half of machine epsilon (On many machines, the lower bound for c is $10^{-3}$ ).

Return Value¶

An array of length nRandom containing the random deviates of a von Mises distribution.

Description¶

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

$f(x) = \frac{1}{2\pi I_0(c)} \exp \left[c \cos(x)\right]$

for $-\pi<x<\pi$ , where $I_0(c)$ is the modified Bessel function of the first kind of order 0. The probability density is equal to 0 outside the interval $\left(-\pi,\pi\right)$ .

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

Example¶

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

from numpy import *
from pyimsl.stat.randomVonMises import randomVonMises
from pyimsl.stat.randomSeedSet import randomSeedSet
from pyimsl.stat.writeMatrix import writeMatrix

n_random = 5
c = 1.0
randomSeedSet(123457)
r = randomVonMises(n_random, c)
writeMatrix("Von Mises random deviates", r, noColLabels=True)

Output¶

 
                   Von Mises random deviates
      0.247       -2.433       -1.022       -2.172       -0.503