Geology topics
Publications and source records attributed to J.R. Wallis.
Distributions whose inverse forms are explicitly defined, such as Tukey's lambda, may present problems in deriving their parameters by more conventional means. Probability weighted moments are introduced and shown to be potentially useful in expressing the parameters of these distributions.
Estimates of the parameters and quantiles of the Gumbel distribution by the methods of probability weighted moments, (conventional) moments, and maximum likelihood were compared. Results were derived from Monte Carlo experiments by using both independent and serially correlated Gumbel numbers. The method of probability weighted moments was seen to compare favorably with the other two techniques.
The applicability of the James-Stein estimator in regional hydrologic studies which entail the estimation of an N -dimensional location parameter is discussed. Regional studies are frequently characterized by relatively short, generally correlated, samples drawn from nonsymmetric and bounded, i.e., nonnormal, populations. By means of computer simulation studies the James-Stein estimator, subject to the Lindley modification and adoption of the positive part rule suggested by Efron and Morris and conditioned on the assumption of independence, was shown to be robust in the case of the hydrologically plausible distribution considered here, namely, Weibull distributions with coefficient of skewness ranging from 0 to 10. However, in contrast to traditional methods of regionalization the effect of cross correlation is a diminishment of the relative risk advantage of the James-Stein estimator, even in the best case of normal variables : this is discussed and illustrated.