LMoment and Probability Plot Correlation Coefficient Goodness-of-fit Tests for the Gumbel Distribution and Impact of Autocorrelation

1995 ◽  
Vol 31 (1) ◽  
pp. 225-229 ◽  
Author(s):  
Heinz D. Fill ◽  
Jery R. Stedinger
Keyword(s):  
Correlation Coefficient ◽  
Goodness Of Fit ◽  
Gumbel Distribution ◽  
Goodness Of Fit Tests ◽  
Probability Plot

scholarly journals Estimating Rainfall Design Values for the City of Oslo, Norway—Comparison of Methods and Quantification of Uncertainty

Water ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 1735 ◽  
Author(s):  
Julia Lutz ◽  
Lars Grinde ◽  
Anita Verpe Dyrrdal
Keyword(s):  
Bayesian Inference ◽  
Goodness Of Fit ◽  
Bayesian Method ◽  
Gumbel Distribution ◽  
Likelihood Estimation ◽  
Current Method ◽  
Credible Interval ◽  
Computational Method ◽  
Goodness Of Fit Tests ◽  
Idf Curves

Due to its location, its old sewage system, and the channelling of rivers, Oslo is highly exposed to urban flooding. Thus, it is crucial to provide relevant and reliable information on extreme precipitation in the planning and design of infrastructure. Intensity-Duration-Frequency (IDF) curves are a frequently used tool for that purpose. However, the computational method for IDF curves in Norway was established over 45 years ago, and has not been further developed since. In our study, we show that the current method of fitting a Gumbel distribution to the highest precipitation events is not able to reflect the return values for the long return periods. Instead, we introduce the fitting of a Generalised Extreme Value (GEV) distribution for annual maximum precipitation in two different ways, using (a) a modified Maximum Likelihood estimation and (b) Bayesian inference. The comparison of the two methods for 14 stations in and around Oslo reveals that the estimated median return values are very similar, but the Bayesian method provides upper credible interval boundaries that are considerably higher. Two different goodness-of-fit tests favour the Bayesian method; thus, we suggest using the Bayesian inference for estimating IDF curves for the Oslo area.

scholarly journals ASSESSMENT OF THE BEST PROBABILITY DISTRIBUTION METHOD IN RAINFALL FREQUENCY ANALYSIS FOR A TROPICAL REGION

2021 ◽  
Vol 33 (1) ◽  
Author(s):  
Stephen Luo Sheng Yong ◽  
Jing Lin Ng ◽  
Yuk Feng Huang ◽  
Chun Kit Ang
Keyword(s):  
Goodness Of Fit ◽  
Gumbel Distribution ◽  
Tropical Region ◽  
Distribution Method ◽  
Maximum Rainfall ◽  
Significance Level ◽  
Type Iii ◽  
Goodness Of Fit Tests ◽  
Passing Rate ◽  
Pearson Type

The Intensity-Duration-Frequency (IDF) curve defines the relationship between rainfall intensities at certain durations and with the frequencies. The IDF Curve is extensively used in many applications such as flood modelling and peak discharge estimation. Over the years, the frequent occurrence of flood has become a great challenge in Kelantan river basin. Herein, IDF curves using frequency analyses based on different distributions were developed and compared. The historical rainfall data at eight rainfall stations for the period of 1985-2019 were selected for the assessment purpose. The Gumbel, Normal and Log Pearson Type III distributions were fitted into the annual maximum rainfall series for durations varying from 30 minutes to 24 hours. The goodness of fit tests were then used to evaluate the performances of each frequency distribution. It was found that the Gumbel distribution gave the highest passing rate followed by the Log Pearson Type III and then the Normal distributions. The Gumbel distribution resulted in respective 86% and 75% passing rate since most of the p-values generated by both the K-S and the Mann-Whitney test were greater than 5% of significance level leading to the acceptance of the null hypothesis. Thus, the Gumbel distribution is suggested for the frequency analyses in this study.

Regression equations of probability plot correlation coefficient test statistics using machine learning

2020 ◽  
Author(s):  
Hyunjun Ahn ◽  
Sunghun Kim ◽  
Joohyung Lee ◽  
Jun-Haeng Heo
Keyword(s):  
Machine Learning ◽  
Probability Distribution ◽  
Sample Size ◽  
Correlation Coefficient ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Model ◽  
Regression Equations ◽  
Probability Plot ◽  
Sample Data

<p>In the extremes hydrology field, it is essential to find the probability distribution model that is most appropriate for the sample data to estimate the reasonable probability quantile. Depending on the assumed probability distribution model, the probability quantile could be estimated with quite different values. The probability plot correlation coefficient (PPCC) test is one of the goodness-of-fit tests for finding suitable probability distributions for a given sample. The PPCC test determines whether assumed probability distributions are acceptable for the sample data using correlation coefficients between sample data and theoretical quantiles of assumed probability distributions. The critical values for identification are presented as a two-dimensional table, depending on the sample size and the shape parameters of models, for a three-parameter probability distribution. In this study, the applicability and utility of machine learning in the hydrology field were examined. For the usability of the PPCC test, a regression equation was derived using a machine learning algorithm with two variables: sample size and shape parameter.</p>

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