gumbelMLE: Maximum Likelihood Estimation for the Gumble Model

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

Description

Solves the score equations for the 2D extremal Poisson process likelihood using the Gumbel like intensity function

Usage

gumbelMLE(x, hessian_tf, ...)

## S3 method for class 'thresholded_series'
gumbelMLE(x, hessian_tf)

## Default S3 method:
gumbelMLE(x, lt, thresh, hessian_tf)

Arguments

x	An S3 object of class thresholded_series or a numeric vector. If the latter, the values used in fitting.
hessian_tf	(logical scalar) Compute the Hessian matrix (TRUE) or not.
lt	(numeric scalar) The length of the time series in units of time (seconds, minutes, hours, etc.).
thresh	(numeric scalar) The threshold for the values

Details

The likelihood is

\Big(∏_{i = 1}^I λ(t_i, y_i)\Big)\exp\Big[-\int_\mathcal{D} λ(t, y)dtdy\Big]

where

λ(t, y) = \frac{1}{σ}\exp\Big[\frac{-(y - μ)}{σ}\Big]

Value

An S3 object of class gumbel_pot_fit with elements

$par

(numeric vector of length 2) The estimated location and scale parameter, respectively

$lhessian

The Hessian matrix at the MLE if requested, else NULL

$y

The observed values used to fit the model

$thresh

The threshold

Methods (by class)

• thresholded_series:

• 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)

## End(Not run)

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