R: Wrapped Normal Maximum Likelihood Estimates

mle.wrappednormal {circular} | R Documentation

## Wrapped Normal Maximum Likelihood Estimates

### Description

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

### Usage

    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), ...)

### Arguments

`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.

### Value

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.

### Author(s)

Claudio Agostinelli with a bug fix by Ana Nodehi

### References

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

### See Also

`mean.circular`

### Examples

    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

[Package circular version 0.4-93 Index]