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