BAMBI (version 2.3.5)

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 $$f(x) = 1/(2\pi I_0 (\kappa)) \exp(\kappa \cos(x - mu))$$ where \(I_0 (\kappa)\) denotes the modified Bessel function of the first kind with order 0 evaluated at the point \(\kappa\).

Examples

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)