invpareto.mle: Inverse Pareto MLE
In distributionsrd: Distribution Fitting and Evaluation

Description Usage Arguments Details Value Examples

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

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

`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.

The Hill estimator equals

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

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

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)