Pareto distribution maximum likelihood estimation

The maximum likelihood estimate of b is the minimum of x and the maximum likelihood estimate of a is 1/(mean(log(x)) - log(b)).

Usage

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

Arguments

x: a (non-empty) numeric vector of data values.
na.rm: logical. Should missing values be removed?
...: currently affects nothing.

Value

mlpareto returns an object of class univariateML. This is a named numeric vector with maximum likelihood estimates for a and b 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 Pareto distribution see Pareto.

References

Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995) Continuous Univariate Distributions, Volume 1, Chapter 20. Wiley, New York.

Examples

mlpareto(precip)
#> Maximum likelihood estimates for the Pareto model 
#>      a       b  
#> 0.6683  7.0000