The maximum likelihood estimate of alpha is the maximum of x +
epsilon (see the details) and the maximum likelihood estimate of
beta is 1/(log(alpha)-mean(log(x))).
mlpower(x, na.rm = FALSE, ...)mlpower returns an object of class
univariateML.
This is a named numeric vector with maximum likelihood estimates for
alpha and beta and the following attributes:
modelThe name of the model.
densityThe density associated with the estimates.
logLikThe loglikelihood at the maximum.
supportThe support of the density.
nThe number of observations.
callThe call as captured my match.call
a (non-empty) numeric vector of data values.
logical. Should missing values be removed?
epsilon is a positive number added to max(x) as an to the
maximum likelihood. Defaults to .Machine$double.eps^0.5.
For the density function of the power distribution see
PowerDist. The maximum likelihood estimator of
alpha does not exist, strictly
speaking. This is because x is supported c(0, alpha) with
an open endpoint on alpha in the extraDistr implementation of
dpower. If the endpoint was closed, max(x) would have been
the maximum likelihood estimator. To overcome this problem, we add
a possibly user specified epsilon to max(x).
Arslan, G. "A new characterization of the power distribution." Journal of Computational and Applied Mathematics 260 (2014): 99-102.
PowerDist for the power density. Pareto for the closely related Pareto distribution.