On the proficient use of GEV distribution: a case study of subtropical monsoon region in India (original) (raw)
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Trends in Sciences
This paper presents an extension of the generalized extreme value (GEV) distribution, based on the T-X family of distributions: Gompertz-generated family of distributions that make the existing distribution more flexible called the Gompertz-general extreme value (Go-GEV) distribution. Some properties of the proposed distribution are introduced, and a new distribution is applied to actual data, namely rainfall in Lopburi Province, by comparing the proposed model with the traditional GEV distribution and estimating the return levels of the rainfall in Lopburi Province. Results showed that the Go-GEV was an alternative flexible distribution for extreme values that fitted with actual data and described the maximum rainfall better than the traditional GEV distribution. The probability density functions of the Go-GEV distribution had various shapes including left-skewed, right-skewed and close to symmetric. Estimation of the return levels of rainfall values in Lopburi Province by the Go-G...
Applicability of extreme value distribution For analysis of rainfall over India
MAUSAM, 2022
Applicability of extreme value type I distribution, for the analysis of annual maximum rainfall over, different parts of the country has been examined. It is observed that this distribution, function is generally applicable in major parts of the country except m the western parts where It has limited applicability, perhaps due to large variation rainfall.
Journal of Pharmacognosy and Phytochemistry, 2019
A statistical analysis of 27 years rainfall data of Kumulur region in Trichy district of Tamil Nadu was conducted using Gumbel distribution and Generalised Extreme Value (GEV) distribution. The method of L-moments was used for determining the parameters for both distributions. Annual maximum rainfall for 2, 3,4, 5 and 7 consecutive days for the available 27 years were analysed and the return levels for four assumed return periods viz. 2, 5, 10 and 25-years were calculated using both the probability distribution functions. The goodness-of-fit of the distributions were analysed by conducting a chi-square test for the observed and expected return levels. The consecutive days maximum rainfall data found to fit best with generalised extreme value distribution. The Empirical Reduction Formula proposed by the Indian Meteorological Department was used for the calculation of short duration for 1-hr, 2-hr, 3-hr, 5-hr, and 8-hr. From the derived short duration rainfall depths, the intensity of the rainfall was calculated. The rainfall Intensity-Duration-Frequency (R-IDF) curves were plotted for the region and the corresponding empirical models were derived.
The analysis of 27 years rainfall data of Kumulur region was conducted using two types of probability distributions, viz Gumbel distribution and generalised extreme value distribution. The method of L-moments was used for the analysis. Annual one day maximum and 2, 3,4, 5 and 7 consecutive days maximum rainfall data for 27 years was analysed and the return levels for 2, 5, 10 and 25-years were calculated using the proposed probability distribution functions. Chisquare test was conducted for comparison of the observed and expected return levels obtained using both the distributions. The statistical analysis revealed that, the annual maxima rainfall data for one day maxima and consecutive days maxima of Kumulur region fits best with the generalised extreme value distribution.
Modeling Extreme Rainfall in Kaduna Using the Generalised Extreme Value Distribution
Science World Journal, 2020
An important statistical distribution use in modeling such extreme events is the generalized extreme value distribution while the generalized Pareto distribution is suitable in modeling threshold excesses of extreme values. In this study, monthly rainfall data from the Nigeria Meteorological Agency in Kaduna are fitted to the generalized extreme value distribution and for a suitable threshold of 251mm, threshold excesses were fitted to the generalized Pareto distribution and a return level computed for 25, 50 and 100 years return period respectively. The threshold excesses follow the Weibull distribution and are bounded above implying that there is a finite value which the maximum above the threshold cannot exceed. For the 25, 50 and 100 years return period, a return level of 350mm, 390mm and 490mm with probability of exceedances of 0.04, 0.02 and 0.01 respectively were observed. The result further show that with the increasing level of rainfall as return period increases, there is ...
Comparison of probability distributions in extreme value analysis of rainfall and temperature data
Environmental Earth Sciences, 2018
Estimation of rainfall for a desired return period is of utmost importance for planning, design and management of hydraulic structures in the project site. This can be achieved by fitting of probability distributions to the recorded Annual 1-day Maximum Rainfall (AMR) data through Rainfall Frequency Analysis (RFA). Method of moments is used for determination of the parameters of probability distributions, which are used in RFA. Chi-square and Kolmogorov-Smirnov tests are applied for checking the adequacy of fitting of the distributions to the recorded AMR data. A diagnostic test of D-index is used for the selection of a suitable distribution for estimation of rainfall. The paper presents the Extreme Value Type-1 distribution is better suited amongst six distributions studied in rainfall estimation for Banswara whereas Generalized Extreme Value distribution for Visakhapatnam.
Extreme Value Modeling and Prediction of Extreme Rainfall: A Case Study of Penang
2010
This paper aims to study the suitability of modeling and predicting extreme rainfall events using only ten years of data. Fitting monthly and half-yearly maximum daily rainfall values to the Generalized Extreme Value (GEV) distribution and fitting rainfall values which exceed a certain threshold to the Generalized Pareto (GP) distribution are used. The parameters are estimated and the tests for stationarity and seasonality are performed. Result shows monthly and half-yearly maximum converges to the GEV distribution and declustering improves the fit to the GP distribution. Return levels estimated using monthly maximum is higher than half-yearly maximum, while return levels from GEV is higher than GP. The return level estimated shows rainfall amount will exceed the maximum rainfall observed in the ten years rainfall data in five years time.
International Journal of Current Microbiology and Applied Sciences , 2019
The analysis of one-day maximum rainfall for 27-years rainfall data in Kumulur region was conducted using Gumbel distribution and Generalized Extreme Value distributions. The parameters of the distributions were estimated using the method of L- moments. Annual one-day maximum rainfall data for 27-years was analyzed and the return levels for 2, 5, 10 and 25-years were calculated using the proposed probability distribution functions. The goodness of fit of the probability distribution was analysed by conducting Chi-square test. It was found that, the annual maxima rainfall data for one day maximum rainfall of Kumulur region fits best with the Generalized Extreme Value distribution. The short duration rainfall depths for 1-hr, 2-hr, 3-hr, 5-hr, and 8-hr were calculated using the Empirical Reduction Formula proposed by the Indian Meteorological Department. The intensity of the obtained rainfall depths was also calculated. The rainfall Intensity-Duration-Frequency (R-IDF) curves were plotted for the region and the corresponding empirical equations were derived.
Journal of Civil Engineering and Urbanism, 2020
Extreme Value Analysis (EVA) of rainfall is considered as one of the important aspects to arrive at a design value for planning, design and management of civil and hydraulic structures. This can be achieved by fitting Probability Distribution (PDs) to the series of observed annual 1-day maximum rainfall data wherein the parameters of PDs are determined by method of moments and L-Moments (LMO). In this paper, a study on comparison of Extreme Value Type-1 (EV1), Extreme Value Type-2, Generalized Extreme Value (GEV) and Generalized Pareto distributions adopted in EVA of rainfall for Anakapalli, Atchutapuram, Kasimkota and Parvada sites is carried out. The selection of best fit PD for EVA of rainfall is made through quantitative assessment by using Goodness-of-Fit (viz., Chisquare and Kolmogorov-Smirnov) and diagnostic (viz., root mean squared error) tests; and qualitative assessment by using the fitted curves of the estimated rainfall. On the basis of evaluation of EVA results through quantitative and qualitative assessments, the study indicates the extreme rainfall given by EV1 (LMO) distribution could be used for the purpose of economical design. The study also indicates the extreme rainfall obtained from GEV (LMO) distribution may be considered for the design of civil and hydraulic structure with little risk involvement.
Stochastic Environmental Research and Risk Assessment, 2012
Extreme rainfalls in South Korea result mainly from convective storms and typhoon storms during the summer. A proper way for dealing with the extreme rainfalls in hydrologic design is to consider the statistical characteristics of the annual maximum rainfall from two different storms when determining design rainfalls. Therefore, this study introduced a mixed generalized extreme value (GEV) distribution to estimate the rainfall quantile for 57 gauge stations across South Korea and compared the rainfall quantiles with those from conventional rainfall frequency analysis using a single GEV distribution. Overall, these results show that the mixed GEV distribution allows probability behavior to be taken into account during rainfall frequency analysis through the process of parameter estimation. The resulting rainfall quantile estimates were found to be significantly smaller than those determined using a single GEV distribution. The difference of rainfall quantiles was found to be closely correlated with the occurrence probability of typhoon and the distribution parameters.