gumbelMultiFit: Maximum Likelihood Estimation of the Gumble Model for Many...

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

Description

Fit the Gumbel like 2D extremal Poisson process for many thresholds

Usage

gumbelMultiFit(x, lt, n_min, n_max, weight_scale, progress_tf = TRUE)

## S3 method for class 'declustered_series'
gumbelMultiFit(x, lt, n_min, n_max,
  weight_scale, progress_tf = TRUE)

## Default S3 method:
gumbelMultiFit(x, lt, n_min, n_max, weight_scale,
  progress_tf = TRUE)

Arguments

x	An S3 object of class declustered_series or a numeric vector. If the latter, the values to be thresholded and used in fitting.
lt	(numeric scalar) The length of the time series in units of time (seconds, minutes, hours, etc.).
n_min	(numeric scalar) The minimum number of thresholded observations to include
n_max	(numeric scalar) The maximum number of thresholded observations to include
weight_scale	(numeric scalar) The value of τ
progress_tf	(logical scalar) Display a progress bar if TRUE, else not.

Details

gumbelMLE and gumbelWPlot are called for a sequence of thresholds. Weights associated with each fit are also calculated. Suppose that for threshold u_i the maximum vertical distance from a point on the W plot to the 45^\circ line is δ_i such that the δ_i are scaled to the unit interval. The weight associated with threshold u_i is then

\frac{\exp\{-τδ_i\}}{∑\exp\{-τδ_i\}}

Value

An S3 object of class gumbel_multi_fit with elements

$all_fits

An object of type gumbel_pot_fit for each threshold

$thresholds

The thresholds for the fits

$weights

The weights associated with the fitted model for each threshold

$lt

The value of the lt argument

$n_min

The value of the n_min argument

$n_max

The value of the n_max argument

$weight_scale

The value of the weight_scale argument

Methods (by class)

• declustered_series:

• default:

Examples

## Not run: 

ddat <- decluster(-jp1tap813wind315$value)

multi_est <- gumbelMultiFit(x = ddat, lt = 100, n_min = 10, n_max = 50, weight_scale = 5)


## End(Not run)

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