univariateML.
This is a named numeric vector with maximum likelihood estimates for
lambda and kappa and the following attributes:
model
The name of the model.
density
The density associated with the estimates.
logLik
The loglikelihood at the maximum.
support
The support of the density.
n
The number of observations.
call
The call as captured my match.call
Arguments
x
a (non-empty) numeric vector of data values.
na.rm
logical. Should missing values be removed?
...
lambda0 an optional starting value for the lambda parameter.
reltol is the relative accuracy requested,
defaults to .Machine$double.eps^0.25. iterlim is a positive integer
specifying the maximum number of iterations to be performed before the
program is terminated (defaults to 100).
Details
For the density function of the Lomax distribution see
Lomax.
The likelihood estimator of the Lomax distribution is unbounded when mean(x^2) < 2*mean(x)^2. When this
happens, the likelihood converges to an exponential distribution with parameter
equal to the mean of the data. This is the natural limiting case for the Lomax
distribution, and it is reasonable to use mlexp in this case.
References
Kleiber, Christian; Kotz, Samuel (2003), Statistical Size
Distributions in Economics and Actuarial Sciences, Wiley Series in
Probability and Statistics, 470, John Wiley & Sons, p. 60
set.seed(3)
mllomax(extraDistr::rlomax(100, 2, 4))
# The maximum likelihood estimator may fail if the data is exponential.if (FALSE) {
set.seed(5)
mllomax(rexp(10))
}