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Establishing acceptance regions for L-moments based goodness-of-fit tests for the Pearson type III distribution

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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.

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Acknowledgment

We gratefully acknowledge the financial support by the National Science Council of Taiwan for a research project which led to results presented in this paper.

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Correspondence to Ke-Sheng Cheng.

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Wu, YC., Liou, JJ., Su, YF. et al. Establishing acceptance regions for L-moments based goodness-of-fit tests for the Pearson type III distribution. Stoch Environ Res Risk Assess 26, 873–885 (2012). https://doi.org/10.1007/s00477-011-0519-z

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