Establishing acceptance regions for L-moments based goodness-of-fit tests for the Pearson type III distribution
Tóm tắt
Goodness-of-fit tests based on the L-moment-ratio diagram for selection of appropriate distributions for hydrological variables have had many applications in recent years. For such applications, sample-size-dependent acceptance regions need to be established in order to take into account the uncertainties induced by sample L-skewness and L-kurtosis. Acceptance regions of two-parameter distributions such as the normal and Gumbel distributions have been developed. However, many hydrological variables are better characterized by three-parameter distributions such as the Pearson type III and generalized extreme value distributions. Establishing acceptance regions for these three-parameter distributions is more complicated since their L-moment-ratio diagrams plot as curves, instead of unique points for two-parameter distributions. Through stochastic simulation we established sample-size-dependent 95% acceptance regions for the Pearson type III distribution. The proposed approach involves two key elements—the conditional distribution of population L-skewness given a sample L-skewness and the conditional distribution of sample L-kurtosis given a sample L-skewness. The established 95% acceptance regions of the Pearson type III distribution were further validated through two types of validity check, and were found to be applicable for goodness-of-fit tests for random samples of any sample size between 20 and 300 and coefficient of skewness not exceeding 3.0.
Tài liệu tham khảo
Abida H, Elouze M (2007) Probability distribution of flood flows in Tunisia. Hydrol Earth Syst Sci Discuss 4:957–981
Ben-Zvi A, Azmon B (1997) Joint use of L-moment diagram and goodness-of-fit test: a case study of diverse series. J Hydrol 198:245–259
D’Agostino RB, Stephens MA (1986) Goodness-of-fit techniques. Marcel Dekker, New York
Haan CT (2002) Statistical methods in hydrology. Iowa State Press, Ames
Haddad K, Rahman A, Green J (2011) Design rainfall estimation in Australia: a case study using L moments and Generalized Least Squares Regression. Stoch Environ Res Risk Assess 25:815–825
Hosking JRM (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc B 52(1):105–124
Hosking JRM, Wallis JR (1993) Some statistics useful in regional frequency analysis. Water Resour Res 29(2):271–281
Hosking JRM, Wallis JR (1997) Regional frequency analysis: an approach based on L-moments. Cambridge University Press, Cambridge
Kottegoda NT (1980) Stochastic water resources technology. Macmillan, London
Liou JJ, Wu YC, Cheng KS (2008) Establishing acceptance regions for L-moments based goodness-of-fit tests by stochastic simulation. J Hydrol 355:49–62
McMahon TA, Srikanthan R (1981) Log Pearson III distribution—is it applicable to flood frequency analysis of Australian streams? J Hydrol 52:139–148
Meshgi A, Khalili D (2009) Comprehensive evaluation of regional flood frequency analysis by L- and LH-moments. I. A re-visit to regional homogeneity. Stoch Environ Res Risk Assess 23:119–135
Önöz B, Bayazit M (1995) Best-fit distributions of largest available flood samples. J Hydrol 167:195–208
Shin H, Jung Y, Jeong C, Heo JH (2011) Assessment of modified Anderson–Darling test statistics for the generalized extreme value and generalized logistic distributions. Stoch Environ Res Risk Assess. doi:10.1007/s00477-011-0463-y
Stedinger JR, Lu LH (1995) Appraisal of regional and index flood quantile estimators. Stoch Environ Res Risk Assess 9(1):49–75
Taiwan Water Resources Agency (TW-WRA) (2000) Technical Code for Hydrological Design (in Chinese). Ministry of Economic Affairs, Taipei, Taiwan
Tsukatani T, Shigemitsu K (1980) Simplified Pearson distributions applied to air pollutant concentration. Atmos Environ 14:245–253
Vogel RM, Fennesset NM (1993) L-moments diagrams should replace product moment diagrams. Water Resour Res 29(6):1745–1752
U.S. Water Resources Council (US-WRS) (1981) Guidelines for determining flood flow frequency, bulletin 17B. Office of Water Data Coordination, U.S. Geological Survey, Reston, Virginia
Yang T, Xu CY, Shao QX, Chen X (2010) Regional flood frequency and spatial patterns analysis in the Pearl River Delta region using L-moments approach. Stoch Environ Res Risk Assess 24:165–182