MLE of the Cauchy and generalised normal distributions with zero location {Rfast2}

MLE of the Cauchy and generalised normal distributions with zero location

Description

MLE of the Cauchy and generalised normal distributions with zero location.

Usage

cauchy0.mle(x, tol = 1e-07) 
gnormal0.mle(x, tol = 1e-06)

Arguments

x

A numerical vector with positive real numbers.

tol

The tolerance level up to which the maximisation stops set to 1e-07 by default.

Details

The Cauchy is the t distribution with 1 degree of freedom. The cauchy0.mle estimates the usual Cauchy distribution, over the real line, but assumes a zero location. The gnormal0.mle estimates the generalised normal distribution assuming a zero location. The generalised normal distribution is also known as the exponential power distribution or the generalized error distribution.

Value

A list including:

iters

The number of iterations required by the Newton-Raphson algorithm.

loglik

The value of the maximised log-likelihood.

scale

The estimated scale parameter of the Cauchy distribution.

param

The estimated scale and shape parameters of the generalised normal distribution.

Author(s)

Michail Tsagris.

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

References

Do M.N. and Vetterli M. (2002). Wavelet-based Texture Retrieval Using Generalised Gaussian Density and Kullback-Leibler Distance. Transaction on Image Processing. 11(2): 146-158.

See Also

censweibull.mle

Examples

x <- rcauchy(150, 0, 2) 
cauchy0.mle(x)

x <- rnorm(200)
gnormal0.mle(x)