Directional (version 5.7)

Density of some circular distributions: Density of some circular distributions

Description

Density of some circular distributions.

Usage

dvm(x, m, k, rads = FALSE, logden = FALSE)
dspml(x, mu, rads = FALSE, logden = FALSE)
dwrapcauchy(x, m, rho, rads = FALSE, logden = FALSE)
dcircpurka(x, m, a, rads = FALSE, logden = FALSE)
dggvm(x, param, rads = FALSE, logden = FALSE)
dcircbeta(x, m, a, b, rads = FALSE, logden = FALSE)
dcardio(x, m, rho, rads = FALSE, logden = FALSE)
dcircexp(x, lambda, rads = FALSE, logden = FALSE)

Value

A vector with the (log) density values of x.

Arguments

x

A vector with circular data.

m

The mean value of the von Mises distribution and of the cardioid, a scalar. This is the median for the circular Purkayastha distribution.

mu

The mean vector, a vector with two values for the "spml".

k

The concentration parameter.

rho

The \(rho\) parameter of the wrapped Cauchy distribution.

a

The \(\alpha\) parameter of the circular Purkayastha distribution or the \(\alpha\) parameter of the circular beta distribution.

b

The \(\beta\) parameter of the circular beta distribution.

lambda

The \(\lambda\) parameter of the circular or wrapped exponential distribution. This must be positive.

param

The vector of parameters of the GGVM distribution as returned by the function ggvm.mle.

rads

If the data are in rads, then this should be TRUE, otherwise FALSE.

logden

If you the logarithm of the density values set this to TRUE.

Author

Michail Tsagris.

R implementation and documentation: Michail Tsagris .

Details

The density of the von Mises, bivariate projected normal, wrapped Cauchy or the circular Purkayastha distributions is computed.

References

Mardia, K. V. and Jupp, P. E. (2000). Directional statistics. Chicester: John Wiley & Sons.

Jammalamadaka, S. R. & Kozubowski, T. J. (2003). A new family of circular models: The wrapped Laplace distributions. Advances and Applications in Statistics, 3(1), 77-103.

See Also

dkent, rvonmises, desag

Examples

x <- rvonmises(500, m = 2.5, k = 10, rads = TRUE)
mod <- circ.summary(x, rads = TRUE, plot = FALSE)
den <- dvm(x, mod$mesos, mod$kappa, rads = TRUE, logden = TRUE )
mod$loglik
sum(den)