fullMaxDist.full_multi_fit: Distribution of the Maximum Using the Full Model with Many...

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 a 2D extremal Poisson process, but without specifying a single threshold.

Usage

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

Arguments

x	An S3 object of class full_multi_fit.
lt_gen	(numeric scalar) Length of each generated series. The units (seconds, minutes, hours, etc.) should be consistent with the value of lt provided to fullMultiFit.
n_mc	(numeric scalar) The number of samples to draw from the mixture distribution of the maximums
progress_tf	(logical scalar) Display a progress bar if TRUE, else not.

Details

The results of fitting a 2D extremal Poisson process for many thresholds are fed into this function. Random processes are repeatedly generated from each fitted model, according to the weights described in fullMultiFit, and the maximum of each random process is recorded. The recoreded maximums represent an iid sample from a mixture of the distributions of maximum values. Each threshold gives rise to a different distribution of the maximum value. Note that the desired length of the processes generated can be different from the length of time over which the data used to fit the models were observed.

Value

An S3 object of class full_max_dist_multi_thresh with elements

$mu

The estimated location parameter for each threshold

$sigma

The estimated scale parameter for each threshold

$k

The estimated tail length parameter for each threshold

$thres

The thresholds

$lt_gen

The value of the lt_gen argument

$n_each

The number of samples drawn from each mixture component. The sum of $n_each should be n_mc

$max_dist

A numeric vector of length n_mc containing the samples from the mixture distribution of the maximums

Examples

## Not run: 

complete_series <- -jp1tap1715wind270$value

declustered_obs <- decluster(complete_series)

full_multi_fit <- fullMultiFit(x = declustered_obs, lt = 100,
                               n_min = 10, n_max = 50,
                               weight_scale = 5, n_starts = 20)

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

## End(Not run)

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