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

##plugins.themes.bootstrap3.article.main##

  •   Itolima Ologhadien

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.


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

References

Beard, L.R., 1943. Statistical analysis in hydrology. Trans. Am. Soc. Cir. Eng., 108: 1110-1160.

Blom, G. (1958). Statistical estimates and transformed beta variables. John Wiley and Sons, New York.

Gringorten, I.I. (1963). “A plotting rule for extreme probability paper.” Journal of Geophysical Research, Vol.68, No. 3, pp. 813-814.

Hirsch, R.M. and Stedinger, J.R., 1987. Plotting positions for historical floods and their precision. Water Resour. Res., 23(4): 715-727.

Guo, S.L. (1990a). “A discussion on unbiased plotting positions for the general extreme value distribution.” Journal of Hydrology, Vol. 121, pp. 33-44.

Shabri, A. (2002). “A comparison of plotting position formulas for the Pearson Type III distribution”, Journal Teknologi, 36©, Jun. 2002: 61 – 74, Universiti Teknologi Malaysia.

In-na, N., and Nguyen, V-T-V. (1989). “An unbiased plotting position formula for the generalized extreme value distribution.” Journal of Hydrology, Vol. 106, pp. 193-209.

Ahn, H., Shin, H., Kim, S., and Heo, J-H. (2020) Comparison on Probability Plot Correlation Coefficient Test Considering Skewness of Sample for the GEV Distribution J. Korea Water Resources Association, Vol. 47, No. 2:161-170, http://dx.doi.org/10.3741/JKWRA.2014 .47.2.161 pISSN 1226-6280 eISSN 2287-6138.

Murugappan, A. Sivaprakasam, S. and Mohan, S. (2017) “Ranking of Plotting Position Formulae in Frequency Analysis of Annual and Seasonal Rainfall at Puducherry, South India”. Global Journal of Engineering Science and Researches, 4(7), 67–76. ISSN 2348–8034.

Stedinger, J.R., Vogel, R.M., Foufoula-Georgiou, E. (1993). Frequency analysis of extreme events. Handbook of Hydrology, D.R. Maidment, de., McGraw-Hill, New York, N.Y., pp. 18.24-18.26.

Kim, S., Shin, H., Joo, K., and Heo, J.-H. (2012). “Development of plotting position for the general extreme value distribution.” Journal of Hydrology, Vol. 475, pp. 259-269.

Hosking, J. R. M. and Wallis, J. R. Regional frequency analysis: An approach based on L-moments. 2005. Cambridge: Cambridge University Press.

Cunnane, C. (1978). “Unbiased plottoing posiions-A review.” Journal of Hydrology, Vol. 37, No. 3/4, pp. 205-222.

Goel, N.K., and De, M. (1993). “Development of unbiased plotting position formula for General Extreme Value distribution.” Stochastic Environmental Research and Risk Assessment, Vol. 7, pp. 1-13.

Weibull, W., 1939. A statistical theory of strength of materials. Ing. Vet. Akad. Handl., No. 151, Generalstabens Litografiska An~tals Forlag, Stockholm.

Harter, H.L., 1984. Another look at plotting positions. Commun. Star., Theory and Methods, Vol.13(13): 1613-1633.

Makkonen, L. (2006). “Plotting Positions in Extreme Value Analysis” Journal od Appl. Meteorol. and Climatol., 45, pp. 334 – 340.

Makkonen, L., Pajari, M. and Tikanmaki, M (2013). Discussion on “Plotting positions for fitting distributions and Exreme Value Analysis”. Canadian. J. Civ. Eng. 40: 927–929.

Connell, R.J. and Mohessen(2015) “ Estimation of plotting position for flood frequency analysis, HWRS, pp. 1-9. https://www.researchgate.net /publication/309177974.

[20] Alam, M.J.B., and Matin, A. (2005) “Study of Plotting Position Formulae for Surma Basin in Bangladesh” Journal of Civil Engineering, 33(1), 9-17.

Chadwick, A., Morfett, J., and Borthwick, M. (2004). Hydraulics in Civil and Environmental Engineering, 4th Edition, ISBN O – 415–39236–5.

Lutz, J., Grinde, L., and Dyrrdal, A.V (2020). “Estimating Rainfall Design Values for the City of Oslo, Norway – Comparison of methods and Quantification of Uncertainty. Water 2020, 12, 1735; doi: 10.3390/w12061735.

Cunnane, C., (1989). Statistical Distribution for Flood Frequency Analysis. Operational Hydrol. Rep. 33, World Meteorological Organisation, Geneva.

Millington, N., Das, S., and Simonovic S. P. (2011). “The Comparison of GEV, Log – Pearson Type 3 and Gumbel Distributions in the Upper Thames River Watershed under Global Climate Models” Department of Civil and Environmental Engineering, The University of Western Ontario, London, Ontario, Canada.

Vogel, R.M. (1986). “The probability plot correlation coefficient test for the normal, lognormal, and Gumbel distributional hypotheses.” Water Resources Research, Vol. 22, No. 4, pp. 587-590.

Moriasi, D.N., Gitau, M.W., Pai, N., and Daggupati. P. (2015). Hydrologic and Water Quality Models: Performance Measures and Evaluation Criteria. Transactions of the American Society of Agricultural and Biological Engineers, Vol. 58(6): 1763-1785.

Masse, B. (2017). “Frequency Analysis and Plotting Positions”, Leadership in Sustainable Infrastructure, HYD725–1 to HYD725-9.

Downloads

Download data is not yet available.

##plugins.themes.bootstrap3.article.details##

How to Cite
[1]
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:https://doi.org/10.24018/ejers.2021.6.4.2468.