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- Title
Establishing acceptance regions for L-moments based goodness-of-fit tests for the Pearson type III distribution.
- Authors
Wu, Yii-Chen; Liou, Jun-Jih; Su, Yuan-Fong; Cheng, Ke-Sheng
- Abstract
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.
- Subjects
L-moments; GOODNESS-of-fit tests; DISTRIBUTION (Probability theory); HYDROLOGY; STOCHASTIC analysis
- Publication
Stochastic Environmental Research & Risk Assessment, 2012, Vol 26, Issue 6, p873
- ISSN
1436-3240
- Publication type
Article
- DOI
10.1007/s00477-011-0519-z