MLE of the Cauchy distribution {cauchypca}

MLE of the Cauchy distribution

Description

MLE of the Cauchy distribution.

Usage

cauchy.mle(x, tol = 1e-07)

Arguments

x

A numerical vector with data.

tol

The tolerance level up to which the maximisation stops set to 1e-09 by default.

Details

Instead of maximising the log-likelihood via a numerical optimiser we have used a Newton-Raphson algorithm which is faster. The Cauchy is the t distribution with 1 degree of freedom.

Value

A list including:

iters

The number of iterations required for the Newton-Raphson to converge.

loglik

The value of the maximised log-likelihood.

param

The vector of the parameters.

Author(s)

Michail Tsagris

R implementation and documentation: Michail Tsagris <[e-mail]>.

References

Johnson, Norman L. Kemp, Adrianne W. Kotz, Samuel (2005). Univariate Discrete Distributions (third edition). Hoboken, NJ: Wiley-Interscience.

https://en.wikipedia.org/wiki/Wigner_semicircle_distribution

See Also

cauchy.pca

Examples

x <- rcauchy(1000)
a <- cauchy.mle(x)