L-moments are analogous to conventional moments in that they are used to calculate quantities which are analogous to the mean, standard deviation, skewness and kurtosis of data. In the L-moment field these terms are called L-mean, L-scale, L-skewness and L-kurtosis to distinguish them from conventional moments. They differ from conventional moments in that they are calculated using Linear combinations of the ordered data, the L in linear is what defines the name as L-moments.

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dbpprop:abstract
  • L-moments are analogous to conventional moments in that they are used to calculate quantities which are analogous to the mean, standard deviation, skewness and kurtosis of data. In the L-moment field these terms are called L-mean, L-scale, L-skewness and L-kurtosis to distinguish them from conventional moments. They differ from conventional moments in that they are calculated using Linear combinations of the ordered data, the L in linear is what defines the name as L-moments. Just as for conventional moments, a theoretical distribution has a set of population L-moments, when estimates of these (sample L-moments) can be defined for a sample from the population. There are two common ways that L-moments are used: As summary statistics for data. As parameter estimations for probability distributions. The latter is most commonly done using maximum likelihood methods, however L-moments provide an alternative method. The former can also be performed using conventional moments, however using L-moments provides many advantages. As an example consider a dataset with few data points and one outlying data value. If the ordinary standard deviation of this data set is taken it will be highly influenced by this one point, however if the L-scale is taken it will be far less sensitive to this data value. Consequently L-moments are far more meaningful when dealing with outliers in data than conventional moments. One example of this is using L-moments as summary statistics in Extreme Value Theory (EVT). Other advantages L-moments have over conventional moments are that they only require a finite L-mean to be meaningful, the higher over L-moments need not be finite. (In fact, the L-mean is identical to the ordinary mean. ) In addition, a finite variance is required in order to obtain finite standard errors for estimates of the L-moments. Some appearances of L-moments in the statistical literature include the book by Hand & Nagaraja (2003, Section 9.9) and a number of papers. A number of favourable comparisons of L-moments with ordinary moments have been reported.
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  • L-moments are analogous to conventional moments in that they are used to calculate quantities which are analogous to the mean, standard deviation, skewness and kurtosis of data. In the L-moment field these terms are called L-mean, L-scale, L-skewness and L-kurtosis to distinguish them from conventional moments. They differ from conventional moments in that they are calculated using Linear combinations of the ordered data, the L in linear is what defines the name as L-moments.
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  • L-moments
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