gumbelWPlot: W plot for the Gumbel Poisson Process Intensity Function

In usnistgov/potMax: Empirical Calculation of the Distribution of the Maximum from a Peaks Over Threshold Process

Description

Plot of W-statistics versus standard exponential quantiles for the Gumbel like intensity function described in gumbelMLE

Usage

gumbelWPlot(x, tf_plot, BW, details, ...)

## S3 method for class 'gumbel_pot_fit'
gumbelWPlot(x, tf_plot, BW, details, ...)

## Default S3 method:
gumbelWPlot(x, y, thresh, tf_plot, BW, details, ...)

Arguments

x	An S3 object of type gumbel_pot_fit or numeric vector of length 2 where the first and second components are μ, σ, respectively.
tf_plot	(logical scalar) Create the plot if TRUE, else not.
BW	(logical scalar) The plot is created in black and white if TRUE, else not
details	(logical scalar) Should details of the calculation be returned as a data.frame
y	(numeric vector) The observations that exceed the threshold, NOT the excesses or differences, but the actual observations

Details

This is the W plot from Chapter 1 of "Extreme Values in Finance, Telecomunications, and the Environment," but modified by taking the limit of the formula for W as the tail length parameter goes to zero

W = \frac{y}{σ}

where y is the excess of (difference from) the threshold.

Value

If details is TRUE, a data.frame with the details of the calculation, else invisibly return the maximum vertical distance from the points of the plot to the 45^\circ line

Methods (by class)

• gumbel_pot_fit:

• default:

Examples

## Not run: 
complete_series <- -jp1tap1715wind270$value

declustered_obs <- decluster(complete_series)

thresholded_obs <- gumbelEstThreshold(x = declustered_obs,
                                     lt = 100,
                                     n_min = 10,
                                     n_max = 100)

gumbel_pot_fit <- gumbelMLE(x = thresholded_obs,
                            hessian_tf = TRUE)

gumbelWPlot(x = gumbel_pot_fit, tf_plot = TRUE, BW = FALSE, details = FALSE)

## End(Not run)

usnistgov/potMax documentation built on May 3, 2019, 2:38 p.m.