MLE of continuous univariate distributions defined on the positive line {Rfast2}

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 [e-mail].

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

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

See Also

zigamma.mle, censweibull.mle

Examples

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