The von Mises Distribution

Density, probability distribution function, quantiles, and random generation for the circular normal distribution with mean \(\mu\) and kappa \(\kappa\).

Usage

rvm(n, mean, kappa)

dvm(theta, mean, kappa, axial = FALSE, log = FALSE)

pvm(theta, mean, kappa, from = NULL, tol = 1e-20)

qvm(p, mean, kappa, from = NULL, tol = .Machine$double.eps^(0.6), ...)

Arguments

n

number of observations. If length(n) > 1, the length is taken to be the number required.

mean

numeric. The mean vector in degrees.

kappa

numeric. Concentration parameter in the range \([0, Inf]\)

theta

numeric. Angular value in degrees

axial

logical. Whether the data are axial, i.e. \(\pi\)-periodical (TRUE, the default) or directional, i.e. \(2 \pi\)-periodical (FALSE).

log

logical. If TRUE, probabilities p are given as \(\log(p)\).

from

if NULL is set to \(\mu-\pi\). This is the value from which the pvm and qvm are evaluated. in degrees.

tol

numeric. The precision in evaluating the distribution function or the quantile.

p

numeric. Vector of probabilities with values in \([0,1]\).

...

parameters passed to stats::integrate().

Value

dvm gives the density, pvm gives the probability of the von Mises distribution function, rvm generates random deviates (in degrees), and qvm provides quantiles (in degrees).

See also

cunif, wnorm, and wcauchy

Examples

set.seed(1)
x <- rvm(5, mean = 90, kappa = 2)

dvm(x, mean = 90, kappa = 2)
#> [1] 0.46942367 0.01695767 0.21318638 0.49589993 0.08107754
dvm(x, mean = 90, kappa = 2, axial = TRUE)
#> [1] 0.71367193 0.14001117 0.06570123 0.88231652 0.01932479

pvm(x, mean = 90, kappa = 2)
#> [1] 0.6542335 0.9908071 0.1148932 0.3986252 0.9568411
qvm(c(.25, .5, .75), mean = 90, kappa = 2)
#> [1]  59.65254  90.00000 120.34746