View source: R/univariate.mle.R

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

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. The generalised normal distribution is also known as the exponential power distribution or the generalized error distribution.

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.

` censweibull.mle `

```
x <- rcauchy(150, 0, 2)
cauchy0.mle(x)
x <- rnorm(200)
gnormal0.mle(x)
```

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