fullMLE: Maximum Likelihood Estimation for the Full Model

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

Description

Maximizes the 2D extremal Poisson process likelihood that uses the full intensity function

Usage

fullMLE(x, n_starts, hessian_tf, ...)

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

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

Arguments

x	An S3 object of class thresholded_series or a numeric vector. If the latter, the values used in fitting.
n_starts	(numeric scalar) The number of random starts to use in the search for the maximum
hessian_tf	(logical scalar) Compute the Hessian matrix (TRUE) or not
lt	(numeric scalar) The length of time over which data were observed in units of time (seconds, minutes, hours, etc.)
thresh	(numeric scalar) The threshold

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}\Big[1 + \frac{k(y - μ)}{σ}\Big]^{-1/k - 1}_+

Value

An S3 object of class full_pot_fit, which contains the estimated parameters $par, the threshold $thresh, the Hessian matrix $lhessian if requested, and the data used for the fit $x.

Methods (by class)

• thresholded_series:

• 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)

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

## End(Not run)

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