wle (version 0.9-91)

wle.wrappednormal: Wrapped Normal Weighted Likelihood Estimates

Description

Computes the weighted likelihood estimates for the parameters of a Wrapped Normal distribution: the mean direction and the concentration parameter (and the scale parameter).

Usage

wle.wrappednormal(x, mu, rho, sd, K, boot = 30, group, num.sol = 1, raf = "HD", smooth = 0.0031, tol = 10^(-6), equal = 10^(-3), min.sd = 0.001, min.k = 10, max.iter = 100, use.smooth = TRUE, alpha=NULL, p = 2,
verbose = FALSE, control.circular=list())
"print"(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

x

a vector. The object is coerced to class circular.

mu

if a values if provided the parameter is considered known.

rho

if a values if provided the parameter (and sd) is considered known.

sd

if a values if provided the parameter (and rho) is considered known.

K

number of elements used to approximate the density of the wrapped normal.

boot

the number of starting points based on boostrap subsamples to use in the search of the roots.

group

the dimension of the bootstap subsamples.

num.sol

maximum number of roots to be searched.

raf

type of Residual adjustment function to be use:

raf="HD": Hellinger Distance RAF,

raf="NED": Negative Exponential Disparity RAF,

raf="SCHI2": Symmetric Chi-Squared Disparity RAF.

smooth

the value of the smoothing parameter.

tol

the absolute accuracy to be used to achieve convergence of the algorithm.

equal

the absolute value for which two roots are considered the same. (This parameter must be greater than tol).

min.sd

minimum value for the sd parameter.

min.k

minimum number of elements used to approximate the density of the wrapped normal.

max.iter

maximum number of iterations.

use.smooth

logical, if TRUE a smoothed model is used, default is TRUE.

alpha

if not NULL overrides the value of p. See the next argument p. This is a different parameterization, alpha=-1/2 provides Hellinger Distance RAF, alpha=-1 provides Kullback-Leibler RAF and alpha=-2 provides Neyman's Chi-Square RAF.

p

this parameter works only when raf="HD". p=2 provide Hellinger Distance RAF, p=-1 provide Kullback-Leibler RAF and p=Inf provide Neyman's Chi-Square RAF.

verbose

logical, if TRUE warnings are printed.

control.circular

the attribute of the resulting objects (mu)

digits

integer indicating the precision to be used.

...

further parameters in print.wle.vonmises.

Value

Returns a list with the following components:

call

the match.call().

mu

the estimate of the mean direction or the value supplied. If num.sol > 1 then mu may have length greater than 1, i.e, one value for each root found.

rho

the estimate of the concentration parameter or the value supplied. If num.sol > 1 then rho may have length greater than 1, i.e, one value for each root found.

sd

the estimate of the standard deviation parameter or the value supplied. If num.sol > 1 then sd may have length greater than 1, i.e, one value for each root found.

tot.weights

the sum of the weights divide by the number of observations, one value for each root found.

weights

the weights associated to each observation, one column vector for each root found.

f.density

the non-parametric density estimation.

m.density

the smoothed model.

delta

the Pearson residuals.

tot.sol

the number of solutions found.

not.conv

the number of starting points that does not converge after the max.iter iteration are reached.

Details

Parameters p and raf will be change in the future. See the reference below for the definition of all the RAF.

References

C. Agostinelli. Robust estimation for circular data. Computational Statistics & Data Analysis, 51(12):5867-5875, 2007.

See Also

circular, mle.wrappednormal.

Examples

x <- c(rwrappednormal(n=50, mu=circular(0), sd=1), rwrappednormal(n=5, mu=circular(pi/2), sd=0.5))
wle.wrappednormal(x, smooth=1/20, group=5)