ffaframework (version 0.1.0)

select_ldistance: L-Distance Method for Distribution Selection

Description

Selects a distribution from a set of candidate distributions by minimizing the Euclidean distance between the theoretical L-moment ratios \((\tau_3, \tau_4)\) and the sample L-moment ratios \((t_3, t_4)\).

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.

Usage

select_ldistance(data, ns_years = NULL, ns_structure = NULL)

Value

A list with the results of distribution selection:

• method: "L-distance".

• 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-distance metrics for each candidate distribution.

• recommendation: The name of the distribution with the smallest L-distance.

Arguments

data

Numeric vector of observed annual maximum series values. Must be strictly positive, finite, and not missing.

ns_years

For NS-FFA only: Numeric vector of observation years corresponding to data. Must be the same length as data and strictly increasing.

ns_structure

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.

Details

For each candidate distribution, this method computes the Euclidean distance between sample L-moment ratios (\(\tau_3\), \(\tau_4\)) and the closest point on the theoretical distribution's L-moment curve. For two-parameter distributions (Gumbel, Normal, Log-Normal), the theoretical L-moment ratios are compared directly with the sample L-moment ratios. The distribution with the minimum distance is selected. If a distribution is fit to log-transformed data (Log-Normal or Log-Pearson Type III), the L-moment ratios for the log-transformed sample are used instead.

References

Hosking, J.R.M. & Wallis, J.R., 1997. Regional frequency analysis: an approach based on L-Moments. Cambridge University Press, New York, USA.

See Also

utils_sample_lmoments(), select_lkurtosis(), select_zstatistic(), plot_lmom_diagram()

Examples

data <- rnorm(n = 100, mean = 100, sd = 10)
select_ldistance(data)