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)).

mlpareto(x, na.rm = FALSE)

Arguments

x	a (non-empty) numeric vector of data values.
na.rm	logical. Should missing values be removed?

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.

See also

Pareto for the Pareto density.

Examples

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