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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.
In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.
For example, the midhinge minus the median is a 3-term L-estimator that measures the skewness, and other differences of midsummaries give measures of asymmetry at different points in the tail. [1] Sample L-moments are L-estimators for the population L-moment, and have rather complex expressions. L-moments are generally treated separately; see ...
In statistics, the method of estimating equations is a way of specifying how the parameters of a statistical model should be estimated.This can be thought of as a generalisation of many classical methods—the method of moments, least squares, and maximum likelihood—as well as some recent methods like M-estimators.
In statistics, an L-statistic is a statistic (function of a data set) that is a linear combination of order statistics; the "L" is for "linear". These are more often referred to by narrower terms according to use, namely: L-estimator, using L-statistics as estimators for parameters; L-moment, L-statistic analogs of the conventional moments
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In statistics, a population is a set of similar items or events which is of interest for some question or experiment. [1] A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of ...
The Gini coefficient was originally developed to measure income inequality and is equivalent to one of the L-moments. A simple summary of a dataset is sometimes given by quoting particular order statistics as approximations to selected percentiles of a distribution.