Abstract
A critical issue in parametric methods of frequency analysis, regardless of the phenomenon being modeled, is that of selection of a form of probability distribution to be applied. When one is interested in continuous distributions there exists little theoretical guidance, other than perhaps that provided by the central limit theorem or the (asymptotic) results of extreme value theory, upon which one may base a choice. This paper, in a very general way, introduces a whole new class of probability models which are referred to as distributions of fractional order statistics. The potential efficacies of various member distributions within the class for hydrologic data analysis are also rationalized in a very intuitive way. Considered in some detail is an application of the theory of fractional order statistics to generalize the Gaussian distribution. Monte Carlo results comparing the performance of the generalized distribution with other common hydrologic models are also set forth.
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