Density, distribution function and random generation for
the matrix-Fisher distribution with concentration
kappa $\kappa$.
Usage
dfisher(r, kappa = 1, nu = NULL, Haar = TRUE)
pfisher(q, kappa = 1, nu = NULL, lower.tail = TRUE)
rfisher(n, kappa = 1, nu = NULL)
Arguments
r,q
vector of quantiles.
n
number of observations. If length(n)>1,
the length is taken to be the number required.
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, $P(X >
x)$.
Value
dfishergives the density
pfishergives
the distribution function
rfishergenerates
random deviates
Details
The matrix-Fisher distribution with concentration kappa
has density
$$C_\mathrm{{F}}(r|\kappa)=\frac{1}{2\pi[\mathrm{I_0}(2\kappa)-\mathrm{I_1}(2\kappa)]}e^{2\kappa\cos(r)}[1-\cos(r)]$$ where
$\mathrm{I_p}(\cdot)$ denotes the Bessel
function of order $p$ defined as
$\mathrm{I_p}(\kappa)=\frac{1}{2\pi}\int_{-\pi}^{\pi}\cos(pr)e^{\kappa\cos
r}dr$.