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

## Description

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

## Usage

 ```1 2 3 4 5``` ```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.

`mean.circular`

## Examples

 ```1 2 3``` ```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 ```

### Example output

```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
```

circular documentation built on May 1, 2019, 7:57 p.m.