Abstract
The determination of appropriate quantile relations between the magnitude of extreme events and the corresponding exceedance probabilities is a prerequisite for optimum design of hydraulic structures. Various plotting position formulae have been proposed for estimating the exceedance probabilities or recurrence in. In this study, eight plotting position formulae recommended for GEV distribution were used for estimating the exceedance probabilities of annual maximum series of River Niger at Baro, Kouroussa and Shintaku hydrological stations. The performance measures of PPCC, RRMSE, PBIAS, MAE and NSE were calculated by applying their individual equations to each pair of observed AMS, arranged in ascending order, and exceedance probabilities calculated using each plotting positions. The result of the study show that Weibull was the best plotting position formula, seconded by Beard and thirdly, In – na and Ngugen. This study underscores the necessity to accurately size water infrastructure. In a recent paper, the author found GEV distribution the best – fit probability distribution model in Nigeria. Thus, the need to develop indepth understanding and accurate estimation of exceedance probabilities and return periods using the GEV distribution. Furthermore, this paper recommends similar studies to be conducted for Pearson Type 3(PR3) and Log Pearson Type 3 (LP3) distributions.
Highlights
INTRODUCTION1Probability plotting positions are used for graphical evaluation of probability distribution models and they serve to relate the magnitude of an event to its corresponding probability of exceedance (or non-exceedance) amongst others
The determination of appropriate quantile relations between the magnitude of extreme events and the corresponding exceedance probabilities is a prerequisite for optimum design of hydraulic structures
A brief review of the cited literature show that the various plotting position formulae differ and with diverse claims by researchers. [16] provided a succinct review and discussions on Plotting Position formulae and observed that the choice of a plotting position formulae should depend on the use, which is to be made of the results, and may depends on the underlying distribution
Summary
Probability plotting positions are used for graphical evaluation of probability distribution models and they serve to relate the magnitude of an event to its corresponding probability of exceedance (or non-exceedance) amongst others. Because of their attractive characteristics, they are widely used in water resource engineering practice. A brief review of the cited literature show that the various plotting position formulae differ and with diverse claims by researchers. The need for this study in determining the best plotting position formula for GEV distribution. Eight unbiased plotting position formulae recommended for GEV distribution are evaluated to find the best for GEV distribution. The parameters of GEV distribution were estimated using probability weighting moments and L-Moments
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