Lomax distribution maximum likelihood estimation

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

mllomax(x, na.rm = FALSE, start = NULL,
  rel.tol = .Machine$double.eps^0.25, iterlim = 100)

Arguments

x	a (non-empty) numeric vector of data values.
na.rm	logical. Should missing values be removed?
start	An optional starting value for the `lambda` parameter. Defaults to `median(x)`.
rel.tol	Relative accuracy requested.
iterlim	A positive integer specifying the maximum number of iterations to be performed before the program is terminated.

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 maximum likelihood estimate will frequently fail to exist. This is due to the parameterization of the function which does not take into account that the density converges to an exponential along certain values of the parameters, see vignette("Distribution Details", package = "univariateML").

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