Study of Unbiased Plotting Position Formulae for the Generalized Extreme Value (GEV) Distribution


  •   Itolima Ologhadien


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.

Keywords: Plotting positions, exceedance probability, performance measures, quantile relations, and GEV distribution


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How to Cite
Ologhadien, I. 2021. Study of Unbiased Plotting Position Formulae for the Generalized Extreme Value (GEV) Distribution. European Journal of Engineering and Technology Research. 6, 4 (Jun. 2021), 94-99. DOI: