MLE of the Cauchy and generalised normal distributions with zero location
MLE of the Cauchy and generalised normal distributions with zero location.
cauchy0.mle(x, tol = 1e-07) gnormal0.mle(x, tol = 1e-06)
x |
A numerical vector with positive real numbers. |
tol |
The tolerance level up to which the maximisation stops set to 1e-07 by default. |
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.
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. |
Michail Tsagris.
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.
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.
x <- rcauchy(150, 0, 2) cauchy0.mle(x) x <- rnorm(200) gnormal0.mle(x)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.