The Atlas used a then relatively new method called "L-moments" to
estimate population distributions from sample data sets. This was one of
the first uses of L-moments on large data sets, but the method is now
being used widely by researchers, including National Oceanic and
Atmospheric Administration meteorologists. The "L" stands for a
linear combination of order statistics. This method has been shown to
provide more reliable population estimates from small sample sizes because
it reduces the influence that one outlier has on the selection of the
population type and parameters.
The first four L-moments are the following expected values of linear combinations:
The first L-moment is the mean of the distribution. The second L-moment is a measure of dispersion, analogous to, but not equal to, the standard deviation. The L-CV, defined by
is a function of L-moments analogous to the coefficient of variation.
include the L-skewness, τ3, and the L-kurtosis, τ4.
As their names imply, these are measures of the skewness and kurtosis of
The sample L-moments are then calculated by
l2 = 2b1 - b0 ,
l3 = 6b2 - 6b1 + b0 ,
l4 = 20b3 -
30b2 + 12b1 - b0;
lr is the sample estimate of λr.
Similarly, the ratios τ, τ3,
and τ4 are estimated
revised 1 Aug 06