L-Moment

An -moment is a linear combination of the expected values of order statistics used to summarize the location, scale, and shape of a probability distribution. If denotes the th order statistic in an independent sample of size , then the th population -moment is

In particular, is the mean, measures scale, and the ratios and measure L-skewness and L-kurtosis, respectively. Population L-moments are finite whenever the distribution has a finite mean, and sample L-moments are generally less sensitive to extreme observations than conventional sample moments.