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Theoretical L-moments of Probability Distributions

Source: R/utils-theoretical-lmoments.R
utils_theoretical_lmoments.Rd

Computes the first four L-moments and L-moment ratios for stationary probability models.

Usage

utils_theoretical_lmoments(distribution, params)

Arguments

distribution

A three-character code indicating the distribution family. Must be "GUM", "NOR", "LNO", "GEV", "GLO", "GNO", "PE3", "LP3", or "WEI".

params

Numeric vector of distribution parameters, in the order (location, scale, shape). The length must be between 2 and 5, depending on the specified distribution and structure.

Value

A numeric vector of with four elements:

  • \(\lambda_1\): L-mean

  • \(\lambda_2\): L-variance

  • \(\tau_3\): L-skewness

  • \(\tau_4\): L-kurtosis

Details

The distributions "GUM", "NOR", "GEV", "GLO", and "WEI" have closed-form solutions for the L-moments and L-moment ratios in terms of the parameters. The distributions "GNO" and "PE3" use rational approximations of the L-moment ratios from Hosking (1997). The L-moments ratios for the "LNO" and "LP3" distributions are should be compared to the log-transformed data and are thus identical to the "NOR" and "PE3" distributions respectively.

References

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

Examples

utils_theoretical_lmoments("GEV", c(1, 1, 1))
#> [1]  1.0000000  0.5000000 -0.3333333  0.1666667