invpareto.mle {distributionsrd}

Inverse Pareto MLE

Description

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

Usage

invpareto.mle(x, xmax = NULL, clauset = FALSE, q = 1)

Arguments

x

data vector

xmax

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

clauset

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

q

Percentage of data to search over (starting from the smallest values), dafults to 1.

Details

The Hill estimator equals

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

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 <- rinvpareto(1e3, k = 1.5, xmax = 5)

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

## Pareto fit with xmin set to its real value
invpareto.mle(x = x, xmax = 5)

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