R: Wrapped Normal Density Function

dwrpnorm {CircStats} | R Documentation

## Wrapped Normal Density Function

### Description

Estimate of the wrapped normal density function.

### Usage

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

### Arguments

`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`.

### Details

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}

### Value

Returns an estimate of the wrapped normal density function.

### References

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

### See Also

rwrpnorm

### Examples

    # 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)

[Package CircStats version 0.2-4 Index]