L-moment
In statistics, L-moments are a sequence of statistics used to summarize the shape of a probability distribution. They are linear combinations of order statistics (L-statistics) analogous to conventional moments, and can be used to calculate quantities analogous to standard deviation, skewness and kurtosis, termed the L-scale, L-skewness and L-kurtosis respectively (the L-mean is identical to the conventional mean). Standardised L-moments are called L-moment ratios and are analogous to standardized moments. Just as for conventional moments, a theoretical distribution has a set of population L-moments. Sample L-moments can be defined for a sample from the population, and can be used as estimators of the population L-moments. Population L-moments For a random variable , the th population L-moment is where denotes the th order statistic (th smallest value) in an independent sample of size from the distribution of and denotes expected value operator. In particular, the first four population L-moments are Note that the coefficients of the th L-moment are the same as in the th term of the binomial transform, as used in the -order finite difference (finite analog to the derivative). The first two of these L-moments have conventional names: is the "mean", "L-mean", or "L-location", is the "L-scale". The