For a random variable X, the rth population L-moment is
where Xk:n denotes the kth order statistic (kth … See more

The sample L-moments can be computed as the population L-moments of the sample, summing over r-element subsets of the sample hence averaging by dividing by the binomial coefficient:
Grouping t… See more

A set of L-moment ratios, or scaled L-moments, is defined by
The most useful of these are called the L-skewness, and the L-kurtosis.
L-moment ratios lie within the interval  ( −1, 1 ) . Tighte… See more

L-moments are statistical quantities that are derived from probability weighted moments (PWM) which were defined earlier (1979). PWM are used to efficiently estimate the parameters of distributions expressable in inverse for… See more

There are two common ways that L-moments are used, in both cases analogously to the conventional moments:
1. As summary statistics for data.
2. To derive estimators for the parameters of probability distributions, … See more

The table below gives expressions for the first two L moments and numerical values of the first two L-moment ratios of some common continuous probability distributions with constant L-moment ratios. More complex ex… See more