MethodologyLmoments The Atlas used a then relatively new method called "Lmoments" to
estimate population distributions from sample data sets. This was one of
the first uses of Lmoments 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 Lmoments are the following expected values of linear combinations:
The first Lmoment is the mean of the distribution. The second Lmoment is a measure of dispersion, analogous to, but not equal to, the standard deviation. The LCV, defined by
is a function of Lmoments analogous to the coefficient of variation.
include the Lskewness, τ_{3}, and the Lkurtosis, τ_{4}.
As their names imply, these are measures of the skewness and kurtosis of
the distribution.
The sample Lmoments are then calculated by l_{2} = 2b_{1}  b_{0 }, l_{3} = 6b_{2}  6b_{1} + b_{0} ,
l_{4} = 20b_{3} 
30b_{2} + 12b_{1}  b_{0}; l_{r} is the sample estimate of λ_{r}.
Similarly, the ratios τ,_{ }τ_{3},
and τ_{4} are estimated
respectively by Return to Main Page, National Drought Atlas revised 1 Aug 06 

