Selects a probability distribution by minimizing the absolute distance between the theoretical L-kurtosis (\(\tau_4\)) and the sample L-kurtosis (\(t_4\)). Only supports 3-parameter distributions.
For NS-FFA: To select a distribution for a nonstationary model, include the
observation years (ns_years) and the nonstationary model structure
(ns_structure). Then, this method will detrend the original, nonstationary data
internally using the data_decomposition() function prior to distribution selection.
select_lkurtosis(data, ns_years = NULL, ns_structure = NULL)A list with the results of distribution selection:
method: "L-kurtosis".
decomposed_data: The detrended dataset used to compute the L-moments. For S-FFA,
this is the data argument. For NS-FFA, it is output of data_decomposition().
metrics: A list of L-kurtosis metrics for each distribution.
recommendation: Name of the distribution with the smallest L-kurtosis metric.
Numeric vector of observed annual maximum series values. Must be strictly positive, finite, and not missing.
For NS-FFA only: Numeric vector of observation years corresponding
to data. Must be the same length as data and strictly increasing.
For NS-FFA only: Named list indicating which distribution parameters are modeled as nonstationary. Must contain two logical scalars:
location: If TRUE, the location parameter has a linear temporal trend.
scale: If TRUE, the scale parameter has a linear temporal trend.
This method computes the distance between the sample and theoretical L-kurtosis
values at a fixed L-skewness. For three parameter distributions, the shape parameter
that best replicates the sample L-skewness is determined using stats::optim().
Hosking, J.R.M. & Wallis, J.R., 1997. Regional frequency analysis: an approach based on L-Moments. Cambridge University Press, New York, USA.
utils_sample_lmoments(), select_ldistance(), select_zstatistic(),
plot_lmom_diagram()
data <- rnorm(n = 100, mean = 100, sd = 10)
select_lkurtosis(data)
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