rotations (version 1.6.5)

Mises: The circular-von Mises distribution

Description

Density, distribution function and random generation for the circular-von Mises distribution with concentration kappa \(\kappa\).

Usage

dvmises(r, kappa = 1, nu = NULL, Haar = TRUE)
pvmises(q, kappa = 1, nu = NULL, lower.tail = TRUE)
rvmises(n, kappa = 1, nu = NULL)

Value

dvmises

gives the density

pvmises

gives the distribution function

rvmises

generates random deviates

Arguments

r, q

vector of quantiles

kappa

concentration parameter.

nu

circular variance, can be used in place of kappa.

Haar

logical; if TRUE density is evaluated with respect to the Haar measure.

lower.tail

logical; if TRUE (default), probabilities are \(P(X \le x)\) otherwise, \(P(X > x)\).

n

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

Details

The circular von Mises distribution with concentration \(\kappa\) has density $$C_\mathrm{M}(r|\kappa)=\frac{1}{2\pi \mathrm{I_0}(\kappa)}e^{\kappa cos(r)}.$$ where \(\mathrm{I_0}(\kappa)\) is the modified Bessel function of order 0.

See Also

Angular-distributions for other distributions in the rotations package.

Examples

r <- seq(-pi, pi, length = 500)

#Visualize the von Mises density fucntion with respect to the Haar measure
plot(r, dvmises(r, kappa = 10), type = "l", ylab = "f(r)", ylim = c(0, 100))

#Visualize the von Mises density fucntion with respect to the Lebesgue measure
plot(r, dvmises(r, kappa = 10, Haar = FALSE), type = "l", ylab = "f(r)")

#Plot the von Mises CDF
plot(r,pvmises(r,kappa = 10), type = "l", ylab = "F(r)")

#Generate random observations from von Mises distribution
rs <- rvmises(20, kappa = 1)
hist(rs, breaks = 10)