FREKANS ANALİZİNDE ALTERNATİF BİR PARAMETRE TAHMİN METODU

Öz

Taşkınlar, sağanaklar ve kurak akımlar gibi ekstrem hidrolojik olayların frekans analizi, su kaynakları sistemlerinin planlanması, boyutlandırılması ve işletilmesi açısından büyük önem arz ettiği gibi, bu ekstrem olayların ekonomik ve sosyal açıdan olumsuz sonuçlarından kaçınma konusunda da büyük fayda sağlamaktadır. Frekans analizinin önemli adımlarından biri uygun dağılım modelinin parametrelerinin tahmin edilmesidir. Bu makalede, merkezi eğilimin robust (sağlam) bir parametresi olan M (medyan), istatistiksel saçılmayı gösteren robust parametre IQR (kuartiller arası uzaklık) ve kuartil çarpıklık katsayısı QCs istatistiklerini kullanan alternatif bir parametre tahmin metodu (RİM) (Robust İstatistikler Metodu) anlatılmaktadır. Çalışma kapsamında, özellikle hidrolojik frekans analizinde yaygın bir şekilde kullanılan altı farklı olasılık dağılım fonksiyonuna (Normal, 2 ve 3 parametreli lognormal, Gamma, Gumbel, ve genelleştirilmiş ekstrem değer GEV) yer verilmiştir. Medyan ve kuartiller arası uzaklık gibi robust istatistiklerin kullanılmasının, aykırı gözlemlerin varlığından veya değişiminden kaynaklanan etkilere karşı daha güvenli parametre tahmini sağlayacağı düşünülmektedir. Çalışmada sayısal örnekler olarak, altı yağış istasyonunun 24 saat süreli yıllık maksimum yağış şiddeti verileri kullanılmıştır. Son olarak, Robust İstatistikler Metodu ile elde edilen parametreler kullanılarak hesaplanan belli olasılıklı tahminler (kuantiller), Maksimum Olabilirlik Metodu, Momentler Metodu ve Olasılık Ağırlıklı Momentler Metodu gibi geleneksel parametre tahmin metotlarıyla elde edilen sonuçlarla karşılaştırılmıştır.

Anahtar Kelimeler

• Hidrolojik Frekans Analizi
• Parametre Tahmin Metotları
• Robust İstatistikler

An Alternative Parameter Estimation Method in Frequency Analysis

Öz

Frequency analysis of extreme hydrologic events such as floods, storms, and droughts provides important information on planning, design, and management of water resources systems, and this information is helpful in avoiding negative economic and social consequences. An important step of the frequency analysis is to estimate the appropriate distribution's parameters. This paper shows the application of an alternative parameter-estimation method, RSM (Robust Statistics Method), which calculates the robust measure of central tendency M (median), statistical dispersion IQR (interquartile range) and quartile coefficient of skewness QCs; and uses these robust statistics by the estimation of the parameters of various distribution functions. Six probability distributions (Normal, 2- and 3- parameter lognormal, Gamma, Gumbel and generalized extreme value GEV), which are commonly used in hydrological frequency analysis were discussed within the study. The advantage of using robust statistics like median and interquartile range in parameter estimation is to ensure the resistance to the effect of a change in value or presence of outlying observations. Numerical analyses as part of this research were carried out on the annual maximum 24h rainfall intensities of rainfall gages in the Aegean Region (Turkey). Eventually, the quantile estimations calculated with the parameters of Robust Statistics Method were compared with the results of conventional methods like Maximum Likelihood, Method of Moments, and Probability-Weighted Moments.

Anahtar Kelimeler

• Frequency Analysis
• Parameter Estimation Methods
• Robust Statistics

Kaynakça

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