fullMaxDist: Distribution of the Maximum Using the Full Model

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

Description

Empirically build the distribution of the maximum value over some user defined length of time assuming the underlying data generating mechanism is the 2D extremal Poisson process with the full intensity function

Usage

fullMaxDist(x, lt_gen, n_mc, progress_tf = TRUE, ...)

## S3 method for class 'full_pot_fit'
fullMaxDist(x, lt_gen, n_mc, progress_tf = TRUE)

## Default S3 method:
fullMaxDist(x, thresh, lt_gen, n_mc,
  progress_tf = TRUE)

Arguments

x	An S3 object of class full_pot_fit or a numeric vector of lenght 3. If the latter the first element of the vector should be the estimated location parameter μ, the second element should be the estimated scale parameter σ, and the thrid element should be the estimated tail length parameter k.
lt_gen	Length of each generated series. The units (seconds, minutes, hours, etc.) should be consistent with the value of lt provided to gumbelMLE.
n_mc	The number of samples to draw from the distribution of the maximum
progress_tf	Display a progress bar if TRUE, else not.
thresh	The threshold

Details

The results of fitting the 2D extremal Poisson process are fed into this function. Random processes are repeatedly generated from the fitted model, and the maximum of each random process is recorded. The recoreded maximums represent an iid sample from the distribution of the maximum value for a process of the desired length. Note that the desired length of the process can be different from the length of time over which the data used to fit the model were observed.

Value

An S3 object of class full_max_dist with elements

$par

The parameters used to generate the random processes

$thres

The threshold used

$lt_gen

The value of the lt_gen argument

$max_dist

A numeric vector of length n_mc containing the samples from the distribution of the maximum

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,
                                    n_starts = 10)

full_pot_fit <- fullMLE(x = thresholded_obs,
                        hessian_tf = TRUE,
                        n_starts = 10)

full_max_dist <- fullMaxDist(x = full_pot_fit, lt_gen = 200, n_mc = 1000)

## End(Not run)

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