halfcauchy.mle: MLE of continuous univariate distributions defined on the... In Rfast2: A Collection of Efficient and Extremely Fast R Functions II

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

MLE of continuous univariate distributions defined on the positive line

Description

MLE of continuous univariate distributions defined on the positive line.

Usage

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

Arguments

 `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.

Details

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.

Value

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.

Author(s)

Michail Tsagris.

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

References

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

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