gumbelNYear.gumbel_multi_fit: Return Values for the Gumbel Model Using Many Thresholds

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, but combining the results over many thresholds

Usage

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

Arguments

x

An S3 object of type gumbel_multi_fit

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 gumbelMultiFit. 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.

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 for many thresholds and combines the results by weighted averaging. The weights are described in the documentation for gumbelMultiFit.

Value

An S3 object of class gumbel_N_year_val_multi_thresh with elements

$mu

A numeric vector containing the estimated location parameters, one for each threshold considered

$sigma

A numeric vector containing the estimated scale parameters, one for each threshold considered

$thresh

A numeric vector containing the thresholds being considered

$N

The value inputted for N

$N_year_val

(numeric scalar) The return value

Examples

## Not run: 

complete_series <- -jp1tap1715wind270$value

declustered_obs <- decluster(complete_series)

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

500_second_val <- gumbelNYear(x = gumbel_multi_fit, N = 500)

## End(Not run)

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