fullWPlot: W plot for the Full 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 full Poisson process intensity function described in fullMLE

Usage

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

## S3 method for class 'full_pot_fit'
fullWPlot(x, tf_plot, BW, details, ...)

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

Arguments

x	An S3 object of type full_pot_fit or numeric vector of length 3 where the first, second, and thrid components are μ, σ, and k, 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." The chapter was authored by Richard Smith. The formula for W is

W = \frac{1}{k}\log\Big\{1 + \frac{ky}{σ + k(u - μ)}\Big\}

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

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)

• full_pot_fit:

• default:

Examples

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

declustered_obs <- decluster(complete_series)

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

full_pot_fit <- fullMLE(x = thresholded_obs,
                        hessian_tf = TRUE)

fullWPlot(x = full_pot_fit, tf_plot = TRUE, BW = FALSE, details = FALSE)

## End(Not run)

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