Lomax distribution maximum likelihood estimation

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. 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).

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

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

Examples

set.seed(3)
mllomax(extraDistr::rlomax(100, 2, 4))
#> Maximum likelihood estimates for the Lomax model 
#> lambda   kappa  
#>  1.054   6.764  

# The maximum likelihood estimator may fail if the data is exponential.
if (FALSE) { # \dontrun{
set.seed(5)
mllomax(rexp(10))
} # }