A1inv {CircStats}

Inverse of A1

Description

Inverse function of the ratio of the first and zeroth order Bessel functions of the first kind. This function is used to compute the maximum likelihood estimate of the concentration parameter of a von Mises distribution.

Usage

A1inv(x)

Arguments

x

numeric value in the interval between 0 and 1.

Details

A1inv(0) = 0 and A1inv(1) = inf. This function is useful in estimating the concentration parameter of data from a von Mises distribution.

Value

Returns the value k, such that A1inv(x) = k, i.e. A1(k) = x.

See Also

est.kappa, A1, besselI.

Examples

#Generate data from a von Mises distribution
data <- rvm(50, pi, 4)
#Estimate the concentration parameter
s <- sum(sin(data))
c <- sum(cos(data))
mean.dir <- atan2(s, c)
kappa <- A1inv(mean(cos(data - mean.dir)))