L-Moment
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A L-Moment is a linear combination of order statistics analogous to a moment-generating function.
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- Counter-Example(s)
- See: L-Estimator, Central Moment, Probability Distribution, Statistical Deviation, Statistical Dispersion.
References
2016
- (Wikipedia, 2016) ⇒ http://en.wikipedia.org/wiki/L-moments Retrieved 2016-08-21
- 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.
(...) L-moments are statistical quantities that are derived from probability weighted moments (PWM) which were defined earlier (1979). PWM are used to efficiently estimate the parameters of distributions expressable in inverse form such as the Gumbel, the Tukey, and the Wakeby distributions.