ffaframework (version 0.1.0)

utils_sample_lmoments: Sample L-moments

Description

Computes the first four sample L-moments and L-moment ratios from a numeric vector of data. L-moments are linear combinations of order statistics that provide robust alternatives to conventional moments, with advantages in parameter estimation for heavy-tailed and skewed distributions.

Usage

utils_sample_lmoments(data)

Value

A numeric vector containing the first four sample L-moments and L-moment ratios:

• \(l_1\): L-mean

• \(l_2\): L-variance

• \(t_3\): L-skewness

• \(t_4\): L-kurtosis

Arguments

data

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

Details

Given probability weighted moments \(\beta_0, \beta_1, \beta_2, \beta_3\), the first four sample L-moments are:

• \(l_1 = \beta_0\)

• \(l_2 = 2\beta_1 - \beta_0\)

• \(l_3 = 6\beta_2 - 6\beta_1 + \beta_0\)

• \(l_4 = 20\beta_3 - 30\beta_2 + 12\beta_1 - \beta_0\)

Then, the sample L-skewness is \(t_3 = l_3 / l_2\) and the sample L-kurtosis is \(t_4 = l_4 / l_2\).

References

Hosking, J. R. M. (1990). L-moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society: Series B (Methodological), 52(1), 105–124.

Examples

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