utils_theoretical_lmoments: Theoretical L-moments of Probability Distributions
Description
Computes the first four L-moments and L-moment ratios for stationary probability models.
Usage
utils_theoretical_lmoments(distribution, params)
Value
A numeric vector of with four elements:
\(\lambda_1\): L-mean
\(\lambda_2\): L-variance
\(\tau_3\): L-skewness
\(\tau_4\): L-kurtosis
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.
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.