gumbelNYearUncert: Uncertainty in Return Values for the Gumbel Model

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

Description

The function produces a bootstrap sample of return values using the Gumbel like 2D extremal Poisson process

Usage

gumbelNYearUncert(x, N, n_boot, ...)

## S3 method for class 'gumbel_pot_fit'
gumbelNYearUncert(x, N, n_boot)

## Default S3 method:
gumbelNYearUncert(x, cov_mat, thresh, N, n_boot)

Arguments

x	An S3 object of type gumbel_pot_fit or a numeric vector of length 2. If the latter, the first element is interpreted as the location parameter μ, and the second element is interpreted as the scale parameter σ.
N	(numeric scalar) The N in N-year return value. This is a bit of a misnomer since the unit of time does not have to be years. The function can calculate N-second, N-minute, N-hour, etc. return values as well. In fact, the unit of time is the same unit of time passed in for the lt argument of gumbelMLE. Naming the function for the unit of time year is simply due to my past experince with calculating return values on the time scale of years.
n_boot	(numeric scalar) The number of bootstrap samples
cov_mat	The covariance matrix used to perturb the estimated parameters. This will most usually be the negative inverse of the Hessian matrix at the MLE

Details

Repeatedly solves the equation

\int_{y_N}^∞\int_0^1λ(t, y)dtdy = \frac{1}{N}

where λ(t, y) is given in the documentation for gumbelMLE for perturbed values of μ and σ. The perturbed values are obtained by using the Hessian matrix and multivariate Guassian distribution to perturb the MLE.

Value

An S3 object of class gumbel_N_year_val_uncert with elements

$par

numeric vector of length 2 containing the location and scale parameters, respectively of the 2D extremal Poisson process used to calculat the return value

$thresh

The threshold

$N

The value inputted for N

$boot_samps

(numeric vector of length n_boot) The bootstrap sample of return values

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)

500_second_val_uncert <- gumbelNYearUncert(x = gumbel_pot_fit, N = 500,
                                           n_boot = 1000)

## End(Not run)

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