gumbelNYear: 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 calculates return values using the Gumbel like 2D extremal Poisson process

Usage

gumbelNYear(x, N, ...)

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

## Default S3 method:
gumbelNYear(x, thresh, N)

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.
thresh	(numeric scalar) The threshold

Details

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

Value

An S3 object of class gumbel_N_year_val 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

$N_year_val

(numeric scalar) The return value

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 <- gumbelNYear(x = gumbel_pot_fit, N = 500)

## End(Not run)

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