mllomax: Lomax distribution maximum likelihood estimation

In JonasMoss/univariateML: Maximum Likelihood Estimation for Univariate Densities

Lomax distribution maximum likelihood estimation

Description

Uses Newton-Raphson to estimate the parameters of the Lomax distribution.

Usage

mllomax(x, na.rm = FALSE, ...)

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. Defaults to median(x). 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 may be unbounded. 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. See vignette("Distribution Details", package = "univariateML") for details.

Value

mllomax returns an object of class 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

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

See Also

Lomax for the Lomax density.

Examples

set.seed(3)
mllomax(extraDistr::rlomax(100, 2, 4))

# The maximum likelihood estimator may fail if the data is exponential.
## Not run: 
set.seed(5)
mllomax(rexp(10))

## End(Not run)

JonasMoss/univariateML documentation built on Nov. 3, 2024, 3:03 p.m.