Cauchy distribution maximum likelihood estimation

Calculates the estimates using nlm and an exponential transform of the location parameter. If n < 5, an exact solution is reported. In the edge case where no maximum likelihood estimator exists and error is thrown.

mlcauchy(x, na.rm = FALSE)

Arguments

x	a (non-empty) numeric vector of data values.
na.rm	logical. Should missing values be removed?

Value

mlcauchy returns an object of class univariateML. This is a named numeric vector with maximum likelihood estimates for location and scale and the following attributes:

model

The name of the model.

density

The density associated with the estimates.

logLik

The loglikelihood at the maximum.

support

The support of the density.

n

The number of observations.

call

The call as captured my match.call

Details

For the density function of the Cauchy distribution see Cauchy.

References

#' @references Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, Volume 1, Chapter 16. Wiley, New York.

See also

Cauchy for the Cauchy density, nlm for the optimizer this function uses.

Examples

mlcauchy(airquality$Temp)
#> Maximum likelihood estimates for the Cauchy model 
#> location     scale  
#>   79.313     5.559