MLE of continuous univariate distributions defined on the positive line
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> and Manos Papadakis <papadakm95@gmail.com>.
N.L. Johnson, S. Kotz \& N. Balakrishnan (1994). Continuous Univariate Distributions, Volume 1 (2nd Edition).
N.L. Johnson, S. Kotz \& N. Balakrishnan (1970). Distributions in statistics: continuous univariate distributions, Volume 2
You can also check the relevant wikipedia pages for these distributions.
x <- abs( rcauchy(1000, 0, 2) ) halfcauchy.mle(x)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.