Generalized Extreme Value Family of Probability Distributions

2012 ◽  
Keyword(s):  
Probability Distributions ◽  
Extreme Value ◽  
Generalized Extreme Value

scholarly journals Hujan rancangan berdasarkan analisis frekuensi regional dengan metode tl-moment

2017 ◽  
Vol 12 (1) ◽  
pp. 1-16
Author(s):  
Segel Ginting ◽  
William M Putuhena
Keyword(s):  
Frequency Analysis ◽  
Probability Distributions ◽  
Large Error ◽  
Extreme Value ◽  
Regional Frequency Analysis ◽  
Generalized Extreme Value ◽  
Generalized Pareto ◽  
Moment Ratio ◽  
Moments Method ◽  
Regional Frequency

The designstorm wereestimated by applying the regional frequency analysis provides benefits to a datasetwith limited amount of data has many advantages. Minimum data used in calculating the amount of design stromhas a very large error for higherreturn period. Therefore, the regional frequency analysis was used based on TL-moments method. There arethree types of probability distributions used in this study, namely the Generalized Extreme Value (GEV), Generalized Pareto (GPA) and the Generalized Logistic (GLO). Two of the three typesprobability distributions are the best choice by the TL-moment ratio diagrams which are Generalized Extreme Value, and Generalized Logistic. Ananother analysis wasconducted by the Z test and the Generalized Extreme Value (GEV) gives the best results. Therefore, the designs strom which was estimated based on the regional frequency analysis in Jakarta watersheds using the Generalized Extreme Value (GEV) has been determined.

scholarly journals Regional analysis of maximum rainfall using L-moment and LH-moment: A comparative case study for the northeast India

MAUSAM ◽  
2021 ◽  
Vol 68 (3) ◽  
pp. 451-462
Author(s):  
DHRUBA JYOTI BORA ◽  
MUNINDRA BORAH ◽  
ABHIJIT BHUYAN
Keyword(s):  
Frequency Analysis ◽  
Moment Method ◽  
Probability Distributions ◽  
Northeast India ◽  
Extreme Value ◽  
Generalized Extreme Value ◽  
Generalized Pareto ◽  
Rainfall Frequency ◽  
Best Fitting ◽  
Rainfall Frequency Analysis

Rainfall data of the northeast region of India has been considered for selecting best fit model for rainfall frequency analysis. The methods of L-moment has been employed for estimation of parameters five probability distributions, namely Generalized extreme value (GEV), Generalized Logistic(GLO), Pearson type 3 (PE3), 3 parameter Log normal (LN3) and Generalized Pareto (GPA) distributions. The methods of LH-moment of four orders (L1 L2, L3 & L4-moments) have also been used for estimating the parameters of three probability distributions namely Generalized extreme value (GEV), Generalized Logistic (GLO) and Generalized Pareto (GPA) distributions. PE3 distribution has been selected as the best fitting distribution using L-moment, GPA distribution using L1-moment and GLO distribution using L2, L3 & L4-moments. Relative root mean square error (RRMSE) and RBIAS are employed to compare between the results found from L-moment and LH-moment analysis. It is found that GPA distribution designated by L1-moment method is the most suitable and the best fitting distribution for rainfall frequency analysis of the northeast India. Also the L1-moment method is significantly more efficient than L-moment and other orders of LH-moment for rainfall frequency analysis of the northeast India.

scholarly journals Comparison of Generalized Extreme Value, Log Normal and Weibull Distributions for Assessment of Low-Flow

2021 ◽  
Vol 11 ◽  
pp. 34-41
Author(s):  
N. Vivekanandan
Keyword(s):  
Goodness Of Fit ◽  
Mean Squared Error ◽  
Probability Distributions ◽  
Water Quality Management ◽  
Extreme Value ◽  
Qualitative Assessment ◽  
Low Flow ◽  
Likelihood Method ◽  
Generalized Extreme Value ◽  
Log Normal

Assessment of low-flow is an important aspect for water quality management, reservoir storage design, determining minimum release policy and safe surface water withdrawals. For which, the annual minimum d-day average flow is generally adopted procedure for characterizing the low-flow in a stream, which can be obtained by averaging the flow using moving average method for ‘d’ consecutive days viz., 7-, 10-, 14- and 30- days. This paper presents a study on comparison of three probability distributions such as Generalized Extreme Value, 2-parameter Log Normal (LN2) and Weibull adopted in estimation of low-flow for river Cauvery at Kollegal gauging site. The parameters are determined by three methods viz., method of moments, maximum likelihood method and L-Moments (LMO), and are used for estimation of low-flow. The adequacy of fitting probability distributions adopted in low-flow frequency analysis is evaluated by quantitative assessment through Goodness-of-Fit (viz., Chi-Square and Kolmogorov-Smirnov) and diagnostic (viz., correlation coefficient and root mean squared error) tests, and qualitative assessment using the fitted curves of the estimated low-flow. The results of quantitative and qualitative assessments indicate that LN2 (LMO) is better suited amongst three distributions adopted in estimation of 7-, 10-, 14- and 30- day low-flows for river Cauvery at Kollegal site.

scholarly journals Evaluation of generalized extreme value and Gumbel distributions for estimating maximum daily rainfall

2021 ◽  
pp. 1-11
Author(s):  
Álvaro José Back ◽  
Fernanda Martins Bonfante
Keyword(s):  
Standard Error ◽  
Probability Distributions ◽  
Daily Rainfall ◽  
Extreme Value ◽  
Mitigation Measures ◽  
Data Series ◽  
Generalized Extreme Value ◽  
Historical Series ◽  
Anderson Darling ◽  
Maximum Daily Rainfall

Extreme rain events can cause social and economic impacts in various sectors. Knowing the risk of occurrences of extreme events is fundamental for the establishment of mitigation measures and for risk management. The analysis of frequencies of historical series of observed rain through theoretical probability distributions is the most commonly used method. The generalized extreme value (GEV) and Gumbel probability distributions stand out among those applied to estimate the maximum daily rainfall. The indication of the best distribution depends on characteristics of the data series used to adjust parameters and criteria used for selection. This study compares GEV and Gumbel distributions and analyzes different criteria used to select the best distribution. We used 224 series of annual maximums of rainfall stations in Santa Catarina (Brazil), with sizes between 12 and 90 years and asymmetry coefficient ranging from -0.277 to 3.917. We used the Anderson–Darling, Kolmogorov-Smirnov (KS), and Filliben adhesion tests. For an indication of the best distribution, we used the standard error of estimate, Akaike’s criterion, and the ranking with adhesion tests. KS test proved to be less rigorous and only rejected 0.25% of distributions tested, while Anderson–Darling and Filliben tests rejected 9.06% and 8.8% of distributions, respectively. GEV distribution proved to be the most indicated for most stations. High agreement (73.7%) was only found in the indication of the best distribution between Filliben tests and the standard error of estimate.

scholarly journals Bicycle Speed Modelling Considering Cyclist Characteristics, Vehicle Type and Track Attributes

2021 ◽  
Vol 12 (1) ◽  
pp. 43
Author(s):  
Xingchen Yan ◽  
Xiaofei Ye ◽  
Jun Chen ◽  
Tao Wang ◽  
Zhen Yang ◽  
...  
Keyword(s):  
Information Criterion ◽  
Lateral Position ◽  
Extreme Value ◽  
Optimal Number ◽  
Generalized Extreme Value ◽  
Vehicle Type ◽  
Lane Width ◽  
Bike Sharing ◽  
Mode Of Transport ◽  
Best Fit

Cycling is an increasingly popular mode of transport as part of the response to air pollution, urban congestion, and public health issues. The emergence of bike sharing programs and electric bicycles have also brought about notable changes in cycling characteristics, especially cycling speed. In order to provide a better basis for bicycle-related traffic simulations and theoretical derivations, the study aimed to seek the best distribution for bicycle riding speed considering cyclist characteristics, vehicle type, and track attributes. K-means clustering was performed on speed subcategories while selecting the optimal number of clustering using L method. Then, 15 common models were fitted to the grouped speed data and Kolmogorov–Smirnov test, Akaike information criterion, and Bayesian information criterion were applied to determine the best-fit distribution. The following results were acquired: (1) bicycle speed sub-clusters generated by the combinations of bicycle type, bicycle lateral position, gender, age, and lane width were grouped into three clusters; (2) Among the common distribution, generalized extreme value, gamma and lognormal were the top three models to fit the three clusters of speed dataset; and (3) integrating stability and overall performance, the generalized extreme value was the best-fit distribution of bicycle speed.

scholarly journals Regional parent flood frequency distributions in Europe – Part 1: Is the GEV model suitable as a pan-European parent?

2014 ◽  
Vol 18 (11) ◽  
pp. 4381-4389 ◽  
Author(s):  
J. L. Salinas ◽  
A. Castellarin ◽  
A. Viglione ◽  
S. Kohnová ◽  
T. R. Kjeldsen
Keyword(s):  
Statistical Model ◽  
Frequency Distribution ◽  
Climatic Factors ◽  
Extreme Value ◽  
Flood Frequency ◽  
Generalized Extreme Value Distribution ◽  
Statistical Hypothesis ◽  
Generalized Extreme Value ◽  
Frequency Distributions ◽  
Hypothetical Scenario

Abstract. This study addresses the question of the existence of a parent flood frequency distribution on a European scale. A new database of L-moment ratios of flood annual maximum series (AMS) from 4105 catchments was compiled by joining 13 national data sets. Simple exploration of the database presents the generalized extreme value (GEV) distribution as a potential pan-European flood frequency distribution, being the three-parameter statistical model that with the closest resemblance to the estimated average of the sample L-moment ratios. Additional Monte Carlo simulations show that the variability in terms of sample skewness and kurtosis present in the data is larger than in a hypothetical scenario where all the samples were drawn from a GEV model. Overall, the generalized extreme value distribution fails to represent the kurtosis dispersion, especially for the longer sample lengths and medium to high skewness values, and therefore may be rejected in a statistical hypothesis testing framework as a single pan-European parent distribution for annual flood maxima. The results presented in this paper suggest that one single statistical model may not be able to fit the entire variety of flood processes present at a European scale, and presents an opportunity to further investigate the catchment and climatic factors controlling European flood regimes and their effects on the underlying flood frequency distributions.

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