gumbelMaxDistUncert: Uncertainty in the Distribution of the Maximum Using the...

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

Description

Evaluate uncertainty in 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 Gumbel like intensity function (i.e. the tail length is zero)

Usage

gumbelMaxDistUncert(x, lt_gen, n_mc, n_boot, progress_tf = TRUE, ...)

## S3 method for class 'gumbel_pot_fit'
gumbelMaxDistUncert(x, lt_gen, n_mc, n_boot,
  progress_tf = TRUE)

## Default S3 method:
gumbelMaxDistUncert(x, cov_mat, thresh, lt_gen, n_mc,
  n_boot, progress_tf = TRUE)

Arguments

x	An S3 object of class gumbel_pot_fit or a numeric vector of lenght 2. If the latter the first element of the vector should be the estimated location parameter μ, and the second element should be the estimated scale parameter σ.
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
n_boot	The number of bootstrap replicates of the distribution of the maximum to create.
progress_tf	Display a progress bar if TRUE, else not.
cov_mat	The covariance matrix to use to perturn the MLE (most usually the negative inverse of the Hessian matrix)
thresh	The threshold

Details

The results of fitting a Gumbel like 2D extremal Poisson process are fed into this function. The Hessian matrix is used to repeatedly perturb the MLE, and for each set of perturbed parameters the distribution of the maximum is empirically constructed as described in gumbelMaxDist. The bootstrap replicates of the distribution of the maximum may be used to quantify uncertainty and construct intervals.

Value

An S3 object of class gumbel_max_dist_uncert with elements

$par

The parameters used to generate the random processes

$cov_mat

The covariance matrix (negative inverse Hessian) used to perturb $par

$thres

The threshold used

$lt_gen

The value of the lt_gen argument

$boot_samps

A matrix n_boot rows and n_mc columns containing the bootstrap replicates of the distribution of the maximum

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)

gumbel_max_dist_uncert <- gumbelMaxDistUncert(x = gumbel_pot_fit, lt_gen = 200,
                                              n_mc = 1000, n_boot = 200)

## End(Not run)

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