Georgia Institute of Technology College of Sciences

L-moments are expectations of certain linear combinations of order statistics. They form the basis of a general theory which covers the summarization and description of theoretical probability distributions, the summarization and description of observed data samples, estimation of parameters and quantiles of probability distributions, and hypothesis tests for probability distributions. L-moments are in analogous to the conventional moments, but are more robust to outliers in the data and enable more secure inferences to be made from small samples about an underlying probability distribution. They can be used for estimation of parametric distributions, and can sometimes yield more efficient parameter estimates than the maximum-likelihood estimates. This talk gives a general summary of L-moment theory and methods, describes some applications ranging from environmental data analysis to financial risk management, and indicates some recent developments on nonparametric quantile estimation, "trimmed" L-moments for very heavy-tailed distributions, and L-moments for multivariate distributions.