pareto.mle {distributionsrd}

Pareto MLE

Description

Maximum likelihood estimation of the Pareto shape parameter using the Hill estimator.

Usage

pareto.mle(x, xmin = NULL, clauset = FALSE, q = 0, lower = 1e-10, upper = Inf)

Arguments

x

data vector

xmin

scale parameter of the Pareto distribution, set to min(x) if not provided

clauset

Indicator variable for calculating the scale parameter using the clauset method, overrides provided xmin

q

Percentage of data to search over (starting from the largest values), defaults to 0.

lower, upper

Lower and upper bounds to the estimated shape parameter, defaults to 1e-10 and Inf respectively

Details

The Hill estimator equals

\hat{k} = \frac{1}{ \frac{1}{n} \sum_{i=1}^{n} log \frac{x_i}{x_{min}}}

Value

Returns a named list containing a

coefficients

Named vector of coefficients

convergence

logical indicator of convergence

n

Length of the fitted data vector

np

Nr. of coefficients

Examples

x <- rpareto(1e3, k = 2, xmin = 2)

## Pareto fit with xmin set to the minium of the sample
pareto.mle(x = x)

## Pareto fit with xmin set to its real value
pareto.mle(x = x, xmin = 2)

## Pareto fit with xmin determined by the Clauset method
pareto.mle(x = x, clauset = TRUE)