# mle.wrappedcauchy: Wrapped Cauchy Maximum Likelihood Estimates In circular: Circular Statistics

## Description

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

## Usage

 ```1 2 3 4``` ```mle.wrappedcauchy(x, mu = NULL, rho = NULL, tol = 1e-15, max.iter = 100, control.circular = list()) ## S3 method for class 'mle.wrappedcauchy' 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 it is coerced to an object of class `circular`. `rho` if `NULL` the maximum likelihood estimate of the concentration parameter is calculated. `tol` precision of the estimation. `max.iter` maximum number of iterations. `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 `convergence` TRUE if convergence is achieved.

## Author(s)

Claudio Agostinelli and Ulric Lund

## 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 <- rwrappedcauchy(n=50, mu=circular(0), rho=0.5) mle.wrappedcauchy(x) # estimation of mu and rho mle.wrappedcauchy(x, mu=circular(0)) # estimation of rho only ```

### Example output

```Attaching package: 'circular'

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

sd, var

Call:
mle.wrappedcauchy(x = x)

mu: 6.219

rho: 0.4555

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

mu: 0

rho: 0.4537

mu is known
There were 50 or more warnings (use warnings() to see the first 50)
```

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