Comparison of parameter estimation methods for the threeparameter generalized pareto distribution

In this paper, the parameter estimation methods of the moments, probability-weighted moments, maximum likelihood, principle of maximum entropy, and least squares to estimate the parameters in the three-parameter generalized Pareto distribution are compared. | Turk J Agric For 29 (2005) 419-428 © TÜB‹TAK Comparison of Parameter Estimation Methods for the ThreeParameter Generalized Pareto Distribution Tekin ÖZTEK‹N University of Gaziosmanpafla, Faculty of Agriculture, Agriculture Technology, Tokat - TURKEY Received: Abstract: The generalized Pareto distribution, which is a special case of both exponential and Wakeby distribution, has good potential for the analysis of flood peaks because of its inherent properties. In this paper, the parameter estimation methods of the moments, probability-weighted moments, maximum likelihood, principle of maximum entropy, and least squares to estimate the parameters in the three-parameter generalized Pareto distribution are compared. The usefulness and applicability of each method is discussed by application to observed annual discharge data for 50 different rivers, most of them in Turkey. The comparisons are based on the ability of each method to predict the elements of the sample series whose non-exceedence probabilities were determined by the Cunnane plotting position formula. Altogether the results demonstrate that for the annual discharge time series considered in this paper the moments method is superior to all the other parameter estimation methods employed. Key Words: three-parameter generalized Pareto distribution, moments, probability-weighted moments, maximum likelihood, principle of maximum entropy, least squares Üç Parametreli Genellefltirilmifl Pareto Da¤›l›m› için Parametre Tahmin Yöntemlerinin Karfl›laflt›r›lmas› Özet: Üstel ve Wakeby da¤›l›mlar›n›n özel bir durumu olan genellefltirilmifl Pareto da¤›l›m›, yap›s›ndaki özelliklerinden dolay› en yüksek debilerin analizi için iyi bir potansiyele sahiptir. Bu makalede, üç parametreli genellefltirilmifl Pareto da¤›l›m› için parametre tahmin yöntemlerinden momentler, olas›l›k a¤›rl›kl› momentler, maksimum olas›l›k, maksimum entropy prensibi ve en küçük kareler yöntemi karfl›laflt›r›lm›flt›r. Her yöntemin .

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