rvm: The univariate von Mises distribution

Description

The univariate von Mises distribution

Usage

rvm(n, kappa = 1, mu = 0)
dvm(x, kappa = 1, mu = 0, log = FALSE)

Value

dvm gives the density and rvm generates random deviates.

Arguments

n: number of observations. Ignored if at least one of the other parameters have length k > 1, in which case, all the parameters are recycled to length k to produce k random variates.
kappa: vector of concentration (inverse-variance) parameters; kappa > 0.
mu: vector of means.
x: vector of angles (in radians) where the densities are to be evaluated.
log: logical. Should the log density be returned instead?

Details

If mu and kappa are not specified they assume the default values of 0 and 1 respectively.

The univariate von Mises distribution has density $f (x) = 1 / (2 π I_{0} (κ)) \exp (κ \cos (x - m u))$ where $I_{0} (κ)$ denotes the modified Bessel function of the first kind with order 0 evaluated at the point $κ$ .

Examples

Run this code


kappa <- 1:3
mu <- 0:2
x <- 1:10
n <- 10


# when x and both parameters are scalars, dvm returns a single density
dvm(x[1], kappa[1], mu[1])

# when x is a vector but both the parameters are scalars, dmv returns a vector of
# densities calculated at each entry of x with the same parameters
dvm(x, kappa[1], mu[1])

# if x is scalar and at least one of the two paraemters is a vector, both parameters are
# recycled to the same length, and dvm returns a vector of with ith element being the
# density evaluated at x with parameter values kappa[i] and mu[i]
dvm(x[1], kappa, mu)

# if x and at least one of the two paraemters is a vector, x and the two parameters are
# recycled to the same length, and dvm returns a vector of with ith element being the
# density at ith element of the (recycled) x with parameter values kappa[i] and mu[i]
dvm(x, kappa, mu)

# when parameters are all scalars, number of observations generated by rvm is n
rvm(n, kappa[1], mu[1])

# when at least one of the two parameters is a vector, both are recycled to the same length,
# n is ignored, and the number of observations generated by rvm is the same as the length of
# the recycled vectors
rvm(n, kappa, mu)