Assessing Symmetry using Quantiles and L-Moments
Résumé
Measures of distributional symmetry based on quantiles, L-moments and trimmed L-moments are briefly reviewed. Sampling properties of commonly used estimators are considered. Approximate standard errors are obtained when sampling from some known distributions. Simulation is used to assess the approximations and indicate the form of the sampling distributions. For sample data, bootstrapped resampling distributions are used to estimate standard errors and make other inferences about the unknown symmetry measure. It is found that symmetry measures based on 2- or 3-trimmed L-moments have some advantages over other measures in terms of their existence and statistical properties of the corresponding estimators.
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