# cauchy0.mle: MLE of the Cauchy and generalised normal distributions with... In Rfast2: A Collection of Efficient and Extremely Fast R Functions II

 MLE of the Cauchy and generalised normal distributions with zero location R Documentation

## 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 mtsagris@uoc.gr.

### 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.

` censweibull.mle `

### Examples

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

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

Rfast2 documentation built on May 29, 2024, 8:45 a.m.