GPD_Fit: Fits a single generalized Pareto distribution - Fit

In rjaneUCF/MultiHazard-R-Package: Tools for modeling compound events

Description

Fit a Generalized Pareto Distribution (GPD) to a declustered dataset.

Usage

GPD_Fit(Data, Data_Full, u = 0.95, mu = 365.25, min.RI = 1,
  PLOT = FALSE, xlab_hist = "Data", y_lab = "Data")

Arguments

Data	Numeric vector containing the declusted data.
Data_Full	Numeric vector containing the non-declustered data.
u	GPD threshold; as a quantile [0,1] of Data vector. Default is 0.95.
mu	Numeric vector of length one specifying (average) occurrence frequency of events in the Data_Full input. Default is 365.25.
min.RI	Numeric vector of length one specifying the minimum return period in the return level plot. Default is 1.
xlab_hist	Character vector of length one. Histogram x-axis label. Default is "Data".
y_lab	Character vector of length one. Histogram x-axis label. Default is "Data".
Plot	Logical; indicating whether to plot diagnostics. Default is FALSE.

Value

List comprising the GPD Threshold, shape parameter xi and scale parameters sigma along with their standard errors sigma.SE and xi.SE.

Details

For excesses of a variable X over a suitably high threshold u the fitted GPD model is parameterized as follows:

P( X > x| X > u) = ≤ft[1 + ξ \frac{(x-u)}{σ}\right]^{-\frac{1}{ξ}}_{+}

where ξ and σ>0 are the shape and scale parameters of the GPD and [y]_{+}=max(y,0).

Examples

Decluster(Data=S20_T_MAX_Daily_Completed_Detrend$Detrend)

rjaneUCF/MultiHazard-R-Package documentation built on Jan. 28, 2021, 12:07 a.m.