Optimization of Parameters in the Generalized Extreme-Value Distribution Type 1 for Three Populations Using Harmonic Search

Molina-Aguilar, Juan Pablo; Gutiérrez-López, Alfonso; Raynal-Villasenor, Jose A.; Garcia-Valenzuela, Luis Gabriel

doi:10.3390/atmos10050257

Cited by 8 publications

(9 citation statements)

References 38 publications

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“…Moretti and Mendes (2003) showed that small samples cause quality loss and less precision in parameter estimates using the method of maximum likelihood. Molina-Aguilar et al (2019) highlighted that multiple methods for estimating the parameters of the Gumbel distribution function are reported in the literature, with the moments and ML methods being the best known and most used of them all.…”

Section: Rbciambmentioning

confidence: 99%

“…Recently, many studies have focused on natural disaster risk analysis with probability distributions based on historical data, which are usually converted to frequencies. Regarding frequency analysis, particularly for extreme events, the objective is to define the events associated with a return period that provide information to carry out the design of hydraulic works, decreasing the uncertainty of the forecast (Molina-Aguilar et al, 2019). Costa et al (2018) commented that studies about the risks of extreme events enable the development of actions that minimize the effects of these events, thus strengthening the resilience of the affected communities, which generally have low technological development to overcome the damage triggered during disasters.…”

Section: Evaluation Of Generalized Extreme Value and Gumbel Distributions For Estimating Maximum Daily Rainfall Introductionmentioning

confidence: 99%

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

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Bonfante

2021

Rev. Bras. Ciênc. Ambient.

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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.

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Section: Rbciambmentioning

confidence: 99%

Section: Evaluation Of Generalized Extreme Value and Gumbel Distributions For Estimating Maximum Daily Rainfall Introductionmentioning

confidence: 99%

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

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Bonfante

2021

Rev. Bras. Ciênc. Ambient.

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“…Optimization algorithms can be effective for optimizing the training of artificial intelligence models [30,31], multi-layer perceptron neural networks [32], and machine learning models [33]. The use of a meta-heuristic technique as a harmonic search was proposed [34]. In this way, new coefficients of Formula (3) are obtained for each hurricane analyzed.…”

Section: Validationmentioning

confidence: 99%

Goes-13 IR Images for Rainfall Forecasting in Hurricane Storms

Meza-Ruiz

Gutiérrez-López

2020

Forecasting

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Currently, it is possible to access a large amount of satellite weather information from monitoring and forecasting severe storms. However, there are no methods of employing satellite images that can improve real-time early warning systems in different regions of Mexico. The auto-estimator is the most commonly used technique that was developed for specific locations in the United States of America (32°–49° latitude) for the type of convective storms. However, the estimation of precipitation intensities for meteorological conditions in tropic latitudes, using the auto-estimator technique, needs to be re-adjusted and calibrated. It is necessary to improve this type of technique that allows decision-makers to have hydro-informatic tools capable of improving early warning systems in tropical regions (15°–25° Mexican tropic latitude). The main objective of the work is to estimate rainfall from satellite imagery in the infrared (IR) spectrum from the Geostationary Operational Environmental Satellite (GOES), validating these estimates with a network of surface rain gauges. Using the GOES-13 IR images every 15 min and using the auto-estimator, a downscaling of six hurricanes was performed from which surface precipitation events were measured. The two main difficulties were to match the satellite images taken every 15 min with the surface data measured every 10 min and to develop a program in C+ that would allow the systematic analysis of the images. The results of this work allow us to get a new adjustment of coefficients in a new equation of the auto-estimator, valid for rain produced by hurricanes, something that has not been done until now. Although no universal relationship has been found for hurricane rainfall, it is evident that the original formula of the auto-estimator technique needs to be modified according to geographical latitude.

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“…Thus, this study considered the three commonly used parameter estimation approaches: the maximum likelihood estimation, the probability weighted moments estimation, and the likelihood moment estimation approaches. It is essential to note that an alternative parameter estimation method, such as the maximum entropy and neural network approaches, have also been proposed by the previous studies [50][51][52][53]. The maximum entropy was used for estimating the parameters of several probability distributions such as gamma, Pearson type III, Log-Pearson type III, and generalized Pareto probability distributions [51,52].…”

Section: Introductionmentioning

confidence: 99%

Flood Frequency Analyses over Different Basin Scales in the Blue Nile River Basin, Ethiopia

Tegegne¹,

Melesse²,

Asfaw³

et al. 2020

Hydrology

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The frequency and intensity of flood quantiles and its attendant damage in agricultural establishments have generated a lot of issues in Ethiopia. Moreover, precise estimates of flood quantiles are needed for efficient design of hydraulic structures; however, quantification of these quantiles in data-scarce regions has been a continuing challenge in hydrologic design. Flood frequency analysis is thus essential to reduce possible flood damage by investigating the most suitable flood prediction model. The annual maximum discharges from six representative stations in the Upper Blue Nile River Basin were fitted to the commonly used nine statistical distributions. This study also assessed the performance evolution of the probability distributions with varying spatial scales, such that three different spatial scales of small-, medium-, and large-scale basins in the Blue Nile River Basin were considered. The performances of the candidate probability distributions were assessed using three goodness-of-fit test statistics, root mean square error, and graphical interpretation approaches to investigate the robust probability distribution for flood frequency analysis over different basin spatial scales. Based on the overall analyses, the generalized extreme value distribution was proven to be a robust model for flood frequency analysis in the study region. The generalized extreme value distribution significantly improved the performance of the flood prediction over different spatial scales. The generalized extreme value flood prediction performance improvement measured in root mean square error varied between 5.84 and 67.91% over other commonly used probability distribution models. Thus, the flood frequency analysis using the generalized extreme value distribution could be essential for the efficient planning and design of hydraulic structures in the Blue Nile River Basin. Furthermore, this study suggests that, in the future, significant efforts should be put to conduct similar flood frequency analyses over the other major river basins of Ethiopia.

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Optimization of Parameters in the Generalized Extreme-Value Distribution Type 1 for Three Populations Using Harmonic Search

Cited by 8 publications

References 38 publications

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

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

Goes-13 IR Images for Rainfall Forecasting in Hurricane Storms

Flood Frequency Analyses over Different Basin Scales in the Blue Nile River Basin, Ethiopia

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