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.

Depth-area relationships, such as those published by the National Weather Service in TP 40 and the NOAA Atlas 2, enable conversion of point rainfall depths to areal average depths for the same storm duration and recurrence interval. This problem of conversion is most germane to hydrologic analyses for moderate to large drainage basins, where point rainfall depths are not representative of the spatial distribution of a storm event. Historically, depth-area relationships have been developed on the basis of data from dense networks of recording gauges. However, with the ongoing accumulation of radar-rainfall records, radar-rainfall data represent an alternative to gauging data. This paper summarizes what is believed to be the first study made under the auspices of the National Weather Service ͑NWS͒ for evaluation of the potential of NEXRAD radar-rainfall data for development of geographically fixed depth-area relationships. Objectives were to evaluate the use of radar-rainfall data for development of depth-area relationships and to identify potential obstacles that might hinder use of such data. Data analyzed for this study are those recorded for the Arkansas-Red Basin River Forecast Center ͑ABRFC͒, and span the period of time from May 1993, to September 2000. Conclusions of this study are that data heterogeneities and shortness of data records are major factors limiting development of depth-area relationships on the basis of radar-rainfall data. Possible biases in radar estimates of extreme rainfall are also of concern. Depth-area curves developed for the ABRFC, presented herein, are reasonably consistent with those presented in NWS publications but should only be considered as preliminary.

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The ability to predict accurately vehicular operating speeds is useful for evaluating the planning, design, traffic operations, and safety of roadways. Operating speed profile (OSP) models are used in the geometric design of highways to evaluate design consistency. Design consistency refers to the condition where the geometric alignment does not violate driver expectations. Existing OSP models have been developed using ordinary linear regression methods. However, the assumptions and limitations inherent to linear regression may at the very least complicate model formulation. If not acknowledged and corrected for, deviations from these assumptions can also adversely affect the efficacies of such models. Artificial neural networks (ANNs) are modeling tools that do not impose the stringent assumptions and limitations imposed by regression. It is therefore of interest to know whether ANNs are viable alter natives to linear regression for OSP modeling. Two backpropagation ANNs for operating speed predictions for passenger cars on two-lane rural highways are evaluated, and their performances with regression-based models are compared. The results of these comparisons indicate that the explanatory powers of the ANN models are comparable with those developed by regression. The predictive powers of the two types of models were observed to be comparable, and ANNs were not limited by distributional or other constraints inherent to regression. Therefore, ANNs were determined to be a viable alternative to regression for OSP model construction.