mle.wrappednormal: Wrapped Normal Maximum Likelihood Estimates
In circular: Circular Statistics

Description Usage Arguments Value Author(s) References See Also Examples

Computes the maximum likelihood estimates for the parameters of a Wrapped Normal distribution: mean and concentration parameter.

mle.wrappednormal(x, mu = NULL, rho = NULL, sd = NULL, K = NULL, 
  tol = 1e-05, min.sd = 1e-3, min.k = 10, max.iter = 100, 
  verbose = FALSE, control.circular=list())
## S3 method for class 'mle.wrappednormal'
print(x, digits = max(3, getOption("digits") - 3), ...)

`x`	a vector. The object is coerced to class `circular`.
`mu`	if `NULL` the maximum likelihood estimate of the mean direction is calculated, otherwise the value is coerced to an object of class `circular`.
`rho`	if `NULL` the maximum likelihood estimate of the concentration parameter is calculated.
`sd`	standard deviation of the (unwrapped) normal. Used as an alternative parametrization.
`K`	number of terms to be used in approximating the density.
`tol`	precision of the estimation.
`min.sd`	minimum value should be reached by the search procedure for the standard deviation parameter.
`min.k`	minimum number of terms used in approximating the density.
`max.iter`	maximum number of iterations.
`verbose`	logical, if `TRUE` information on the convergence process are printed.
`control.circular`	the attribute of the resulting objects (`mu`)
`digits`	integer indicating the precision to be used.
`...`	further arguments passed to or from other methods.

Returns a list with the following components:

`call`	the `match.call` result.
`mu`	the estimate of the mean direction or the value supplied as an object of class `circular`.
`rho`	the estimate of the concentration parameter or the value supplied
`sd`	the estimate of the standard deviation or the value supplied.
`est.mu`	TRUE if the estimator is reported.
`est.rho`	TRUE if the estimator is reported.
`convergence`	TRUE if the convergence is achieved.

Claudio Agostinelli with a bug fix by Ana Nodehi

Jammalamadaka, S. Rao and SenGupta, A. (2001). Topics in Circular Statistics, Section 4.2.1, World Scientific Press, Singapore.

mean.circular

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x <- rwrappednormal(n=50, mu=circular(0), rho=0.5)
mle.wrappednormal(x) # estimation of mu and rho (and sd)
mle.wrappednormal(x, mu=circular(0)) # estimation of rho (and sd) only

Attaching package: 'circular'

The following objects are masked from 'package:stats':

    sd, var


Call:
mle.wrappednormal(x = x)

mu: 0.2186 

rho: 0.6995 

sd: 0.8454 


Call:
mle.wrappednormal(x = x, mu = circular(0))

mu: 0 

rho: 0.683 

sd: 0.8732 

mu is known