sumplot: Sum Plot
In tea: Threshold Estimation Approaches

Description Usage Arguments Details Value References Examples

An implementation of the so called sum plot proposed in de Sousa & Michailidis (2004)

1	sumplot(data, kmin = 5)

`data`	vector of sample data
`kmin`	gives the minimal `k` for which the graph is plotted. Default ist set to `kmin=5`.

The sum plot is based on the plot (k,S_k) with S_k:=k*gamma_k where gamma_k denotes the Hill estimator. So the sum plot and the Hill plot are statistically equivalent. The sum plot should be approximately linear for the k-values where gamma_k=gamma. So the linear part of the graph can be used as an estimator of the (inverse) tail index. The sum plot leads to the estimation of the slope while the classical Hill plot leads to estimation of the intercept. The optimal number of order statistics, also known as the threshold, can then be derived as the value k where the plot differs from a straight line with slope gamma. See references for more information.

The plot shows the values of S_k=k*gamma_k for different k. See references for more information.

De Sousa, Bruno and Michailidis, George (2004). A diagnostic plot for estimating the tail index of a distribution. Journal of Computational and Graphical Statistics 13(4), 1–22.