GPD_Fit | R Documentation |
Fit a Generalized Pareto Distribution (GPD) to a declustered dataset.
GPD_Fit(
Data,
Data_Full,
u = 0.95,
Thres = NA,
mu = 365.25,
GPD_Bayes = TRUE,
Method = "Standard",
min.RI = 1,
PLOT = FALSE,
xlab_hist = "Data",
y_lab = "Data"
)
Data |
Numeric vector containing the declusted data. |
Data_Full |
Numeric vector containing the non-declustered data. |
u |
GPD threshold expressed as a quantile |
Thres |
GPD threshold expressed on the original scale of the |
mu |
Numeric vector of length one specifying (average) occurrence frequency of events in the |
GPD_Bayes |
Logical; indicating whether to use a Bayesian approach to estimate GPD parameters. This involves applying a penalty to the likelihood to aid in the stability of the optimization procedure. Default is |
Method |
Character vector of length one specifying the method of choosing the threshold. |
min.RI |
Numeric vector of length one specifying the minimum return period in the return level plot. Default is |
xlab_hist |
Character vector of length one. Histogram x-axis label. Default is |
y_lab |
Character vector of length one. Histogram x-axis label. Default is |
Plot |
Logical; indicating whether to plot diagnostics. Default is |
List comprising the GPD Threshold
, shape parameter xi
and scale parameters sigma
along with their standard errors sigma.SE
and xi.SE
.
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) = \left[1 + \xi \frac{(x-u)}{\sigma}\right]^{-\frac{1}{\xi}}_{+}
where \xi
and \sigma>0
are the shape and scale parameters of the GPD and [y]_{+}=max(y,0)
.
Decluster(Data=S20_T_MAX_Daily_Completed_Detrend$Detrend)
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