Selects the best-fit distribution by comparing a bias-corrected Z-statistic for the sample L-kurtosis (\(\tau_4\)) against the theoretical L-moments for a set of candidate distributions. The distribution with the smallest absolute Z-statistic is selected.
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_zstatistic(data, ns_years = NULL, ns_structure = NULL, samples = 10000L)A list with the results of distribution selection:
method: "Z-selection".
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: List of computed Z-statistics for each candidate distribution.
recommendation: Name of the distribution with the smallest Z-statistic.
reg_params: Kappa distribution parameters for the data.
reg_bias_t4: Bias of the L-kurtosis from the bootstrap.
reg_std_t4: Standard deviation of the L-kurtosis from the bootstrap.
log_params: Kappa distribution parameters for the log-transformed data.
log_bias_t4: Bias of the L-kurtosis from the bootstrap using log_params.
log_std_t4: Standard deviation of the L-kurtosis from the bootstrap using log_params.
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.
Integer scalar. The number of bootstrap samples. Default is 10000.
First, this method fits a four-parameter Kappa distribution to both the original and log-transformed data. Then, bootstrapping is used to estimate the bias and variance of the L-kurtosis. These values, along with the difference between the sample and theoretical L-kurtosis, are used to compute the Z-statistic for each distribution.
Hosking, J.R.M. & Wallis, J.R., 1997. Regional frequency analysis: an approach based on L-Moments. Cambridge University Press, New York, USA.
select_ldistance(), select_lkurtosis(), fit_lmoments_kappa(),
utils_quantiles(), plot_lmom_diagram()
data <- rnorm(n = 100, mean = 100, sd = 10)
select_zstatistic(data)
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