Wolf-Dieter Richter
Approximating Large Quantiles
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
60F10 Large deviations
Abstract: Asymptotic expansions for probabilities of large deviations are
used to construct an iteration procedure for approximating quantiles in the
far tails of a distribution. Expansions for analytically known distributions are
based on Laplace's method while quantile approximation for the arithmetical
mean relies on large deviation results of the Linnik type. A comparison of
quantile approximation based upon the \delta-method or upon Cornish-Fisher
type expansions with those based upon our large deviation approach show
both formal similarities an substantial differences.
Keywords: Poincare type expansion, large deviation iteration procedure, large deviations in Linnik's zones, skewness-kurtosis adjusted quantiles, adjustments for the arithmetical mean, refined \delta-method quantile approximation