dwrpnorm: Wrapped Normal Density Function
In CircStats: Circular Statistics, from "Topics in Circular Statistics" (2001)

Description Usage Arguments Details Value References See Also Examples

Estimate of the wrapped normal density function.

1	dwrpnorm(theta, mu, rho, sd=1, acc=1e-5, tol=acc)

`theta`	value at which to evaluate the density function, measured in radians.
`mu`	mean direction of distribution, measured in radians.
`rho`	mean resultant length of distribution.
`sd`	different way of select `rho`, see details below.
`acc`	parameter defining the accuracy of the estimation of the density. Terms are added to the infinite summation that defines the density function until successive estimates are within `acc` of each other.
`tol`	the same as `acc`.

The form of the wrapped normal density function is an infinite series with index going from negative infinity to positive infinity. This function begins with the zeroth term and adds terms to the series, corresponding to both the positive and negative index, until the summation changes by less than the parameter value of acc. You can set rho by using sd with the following equivalence:

ρ = \exp{- σ^2/2}

Returns an estimate of the wrapped normal density function.

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 2.2.6, World Scientific Press, Singapore.

rwrpnorm

# Values for which to evaluate density
theta <- c(1:500)*2*pi/500
#Compute wrapped normal density function
density <- c(1:500)
for(i in 1:500) density[i] <- dwrpnorm(theta[i], pi, .75)
plot(theta, density)
#Approximate area under density curve
sum(density*2*pi/500)