heavytails (version 0.1.1)

moments_estimator: Moments Estimator

Description

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

Usage

moments_estimator(data, k, na.rm = FALSE, eps = 1e-12)

Value

A single numeric scalar: Moments 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.

eps

numeric, factor added to the denominator to avoid division by zero. Default value is 1e-12.

Details

$$\hat \xi_{ME} = \underbrace{\hat \xi_{k,n}^{H,1}}_{T_1} + \underbrace{1 - \frac{1}{2}(1-\frac{(\hat \xi_{k,n}^{H,1})^2}{\hat \xi_{k,n}^{H,2}})^{-1}}_{T_2}$$

References

Dekkers, A. L. M., Einmahl, J. H. J., & De Haan, L. (1989). A Moment Estimator for the Index of an Extreme-Value Distribution. The Annals of Statistics, 17(4), 1833–1855. http://www.jstor.org/stable/2241667

Nair, J., Wierman, A., & Zwart, B. (2022). The Fundamentals of Heavy Tails: Properties, Emergence, and Estimation. Cambridge University Press. (pp. 216-219) tools:::Rd_expr_doi("10.1017/9781009053730")

Examples

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