heavytails (version 0.1.1)

pickands_estimator: Pickands Estimator

Description

Pickands estimator to calculate \(\xi\) for the input data.

Usage

pickands_estimator(data, k, na.rm = FALSE)

Value

A single numeric scalar: Pickands estimator calculation of the shape parameter \(\xi\).

Arguments

data

A numeric vector of i.i.d. observations.

k

An integer specifying the number of top order statistics to use (the size of the tail). Must be strictly less than the sample size.

na.rm

Logical. If TRUE, missing values (NA) are removed before analysis. Defaults to FALSE.

Details

$$\hat{\xi}_{P} = \frac{1}{\log 2} \log ( \frac{X_{(k)} - X_{(2k)}}{X_{(2k)} - X_{(4k)}})$$

References

Pickands, J. (1975). Statistical Inference Using Extreme Order Statistics. The Annals of Statistics, 3(1), 119–131. http://www.jstor.org/stable/2958083

Nair, J., Wierman, A., & Zwart, B. (2022). The Fundamentals of Heavy Tails: Properties, Emergence, and Estimation. Cambridge University Press. (pp. 219-221) tools:::Rd_expr_doi("10.1017/9781009053730")

Examples

xmin <- 1
alpha <- 2
r <- runif(800, 0, 1)
x <- (xmin * r^(-1/(alpha)))
pickands <- pickands_estimator(data = x, k = 5)