View source: R/univariate.mle.R

MLE of continuous univariate distributions defined on the positive line | R Documentation |

MLE of continuous univariate distributions defined on the positive line.

```
halfcauchy.mle(x, tol = 1e-07)
powerlaw.mle(x)
```

`x` |
A vector with positive valued data (zeros are not allowed). |

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

Instead of maximising the log-likelihood via a numerical optimiser we have used a Newton-Raphson algorithm which is faster. See wikipedia for the equations to be solved. For the power law we assume that the minimum value of x is above zero in order to perform the maximum likelihood estimation in the usual way.

Usually a list with three elements, but this is not for all cases.

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

`loglik` |
The value of the maximised log-likelihood. |

`scale` |
The scale parameter of the half Cauchy distribution. |

`alpha` |
The value of the power parameter for the power law distribution. |

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

N.L. Johnson, S. Kotz and N. Balakrishnan (1994). Continuous Univariate Distributions, Volume 1 (2nd Edition).

N.L. Johnson, S. Kotz and N. Balakrishnan (1970). Distributions in statistics: continuous univariate distributions, Volume 2

You can also check the relevant wikipedia pages for these distributions.

```
zigamma.mle, censweibull.mle
```

```
x <- abs( rcauchy(1000, 0, 2) )
halfcauchy.mle(x)
```

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.