scholarly journals Modelos probabilísticos para eventos de precipitações extremas na Cidade de Palmares-PE (Probabilistic modeling for extreme rainfall events in the city of Palmares - PE)

2019 ◽  
Vol 12 (4) ◽  
pp. 1355
Author(s):  
Lucas Ravellys Pyrrho De Alcântara ◽  
Artur Paiva Coutinho ◽  
Severino Martins Dos Santos Neto ◽  
Tássia Dos Anjos Tenório de Melo ◽  
Larissa Fernandes Costa ◽  
...  
Keyword(s):  
Extreme Values ◽  
Gumbel Distribution ◽  
Coefficient Of Determination ◽  
Chi Square ◽  
Extreme Rainfall Events ◽  
Extreme Precipitation Events ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Log Normal ◽  
The City

A estimava da probabilidade de excedência de eventos de precipitações pluviométricas máximas pode ser realizada a partir da associação entre as séries hidrológicas e modelos probabilísticos. O presente trabalho tem por objetivo avaliar a aderência da distribuição empírica de Precipitações Diárias Máximas Anuais (PDMA), as distribuições teóricas de probabilidade de Gumbel, Log-Normal de dois parâmetros, Generalizada de Valores Extremos, Fréchet, Weibull para 2 e 3 parâmetros, Gama, Pearson e Log-Pearson para 3 parâmetros. Foi utilizada uma série histórica de precipitação máxima diária anual oriunda da cidade de Palmares-PE, a partir de dados obtidos da Agência Nacional de Águas (ANA). Para avaliar a qualidade de aderência das distribuições, foram utilizados os testes de aderência de Anderson Darling (AD), Kolmogorov-Smirnov (KS) e o teste Qui-Quadrado de Pearson (χ2). Para quantificação da qualidade dos ajustes estatísticos utilizou-se do coeficiente de determinação (R2). As distribuições de Fréchet e Weibull II não apresentaram aderência a distribuição empírica de frequência.  A distribuição de Gumbel foi a que apresentou maior aderência à distribuição empírica de acordo com o teste Qui-Quadrado de Pearson (χ2), enquanto que a GVE e a Pearson III aos testes AD e KS, respectivamente.  A B S T R A C TTo analyze and estimate the likelihood of new extreme precipitation events, hydrological data records and probabilistic mathematical modeling can be used associated with different recurrence frequencies. The objective of this study was to adjust the PDMA of the city of Palmares-PE, based on data obtained from the National Water Agency (ANA), the Gumbel probability distributions, Log-Normal of two Parameters, Generalized Extreme Values, Fréchet, Weibull for 2 and 3 parameters, Range, Pearson and Log-Pearson for 3 parameters. In order to evaluate the statistical distributions, the Anderson Darling (AD), Kolmogorov-Smirnov (KS) and Pearson Chi-Square (χ2) tests were used, and the quantification of the quality of the statistical adjustments was done using coefficient of determination (R2). Among the probabilistic distributions analyzed, the only ones that do not fit are the distributions of FRÉCHET and Weibull II. The Gumbel distribution was the best fit for Pearson Chi-square test (χ2), and GVE and Pearson III, respectively, for the AD and KS tests.Keywords: hydrology statistics, return time, intense rain, extreme events, random variables.

scholarly journals Probability distribution of heavy rainfall and determination of IDF in the city of Caruaru – PE

2021 ◽  
Vol 16 (1) ◽  
pp. 1
Author(s):  
Kevin Matheus Correia Mendes ◽  
Aline Lima de Oliveira ◽  
Lucas Ravellys Pyrrho de Alcântara ◽  
Adriana Thays Araújo Alves ◽  
Severino Martins dos Santos Neto ◽  
...  
Keyword(s):  
Quality Parameters ◽  
Likelihood Method ◽  
Chi Square ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
The Moment ◽  
Log Normal ◽  
The City

In the design of hydraulic engineering works, the estimation of project precipitation is fundamental. Rain forecasting depends on several factors, which makes estimating it simpler with stochastic processes. In this sense, the distributions of Gumbel (GUM), Log-Normal two-parameter (LN2P), Generalized Extreme Value (GEV), Fréchet with two and three parameters (FRE2P and FRE3P), Weibull with two and three parameters (W2P and W3P), Gamma (GAM2P), and Pareto with two and three parameters (PAR2P and PAR3P) were evaluated to the annual maximum daily precipitation (AMDP) adjustment in the city of Caruaru (Pernambuco´s Agreste). A series of AMDP was used, based on data obtained from the National Water Agency (Agência Nacional de Águas - ANA). Anderson Darling (AD), Kolmogorov-Smirnov (KS) and Pearson Chi-square (χ2) adherence tests, and the determination coefficient (R²) were used to assess the adherence quality of the distributions. The Likelihood Method presented a better fit quality than the Moment Method. The GEV distribution obtained the best results for the AD test in both methods to estimate the parameters. Among the adherence tests used, the AD test was considered the most restrictive. To verify the quality parameters’ fitness to the IDF relations, the Willmott performance coefficient was used. For all distributions employed in this study, Willmott performance coefficients presented values above 0.99, giving a perfect fit of IDF relations with determination coefficients close to 1.0.

scholarly journals DETERMINAÇÃO DA CURVA DE INTENSIDADE, DURAÇÃO E FREQUÊNCIA DO MUNICÍPIO DE IPAMERI – GOIÁS

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
Daniela Carneiro Pereira ◽  
Letícia Rodrigues Duarte ◽  
Antover Panazzolo Sarmento
Keyword(s):  
Gumbel Distribution ◽  
Coefficient Of Determination ◽  
Chi Square ◽  
Significance Level ◽  
Maximum Precipitation ◽  
Reduced Gradient Method ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Heavy Rains

RESUMO: A caracterização das chuvas intensas para utilização em projetos de engenharia é fundamental, especificadamente no que tange à obras hidráulicas. O estudo das chuvas intensas é feito por meio da relação entre a intensidade, a duração e a frequência das mesmas. Este artigo trata da determinação de tais relações para o município de Ipameri, Goiás, devido à falta de estudos relacionados a esta localidade. Foi feito o ajustamento à distribuição estatística de Gumbel de forma a obter os valores de precipitação máxima para os períodos de retorno de 2, 5, 10, 15, 20, 25, 50 e 100 anos. Para verificação do ajuste dos dados observados a distribuição de Gumbel, realizou-se os testes de aderência de Kolmogorov-Smirnov, Anderson-Darling e Qui-Quadrado, ao nível de significância de 1%. A desagregação dos valores de precipitação máxima em durações menores que 24 horas foi feita utilizando o método das Relações de Durações. Os parâmetros K (881,7487), a (0,1333), b (10,5332) e c (0,7519) da equação de chuvas intensas foram obtidos utilizando o método do Gradiente Reduzido Generalizado. Para avaliação da equação obtida foi utilizado o coeficiente de determinação (R²), o índice de concordância de Willmott (d) e índice de confiança (Ic), com resultados respectivos de 0,9986, 0,9997 e 0,9990. Assim esta pesquisa contribuiu para a determinação da equação de chuvas intensas, permitindo seu uso no dimensionamento de estruturas hidráulicas do local.ABSTRACT: Heavy rains characterization for use in engineering design projects is essential, specifically with regard to the hydrological researches and structures. In this way the study of heavy rains is done relating the intensity, duration and frequency of the events. This paper deals with the determination of such relations for the city of Ipameri, Goiás - Brazil, due to lack of studies related to the municipality. Adjusting the statistical Gumbel distribution in order to obtain maximum precipitation values for return periods of 2, 5, 10, 15, 20, 25, 50 and 100 years is made. To check the adjustment of the data observed distribution of Gumbel, we held the adherence tests (Kolmogorov-Smirnov, Anderson-Darling and Chi-Square) at a significance level of 1%. The disaggregation of the maximum precipitation values in smaller duration than 24 hours were made using the method of durations relations. The parameters K (881.7487), a (0.1333), b (10.5332) and c (0.7519) of equation heavy rains were obtained using the Generalized Reduced Gradient method. To validate the obtained equation was used the coefficient of determination (R²), the concordance index of Willmott (d) and confidence index (Ic) with the results of 0.9986, 0.9997 and 0.9990. Thus, this research contributes to the determination of the intense rainfall equation, allowing its use in the design of local hydraulic structures.

scholarly journals Statistical Analysis of Natural Events in the United States

1991 ◽  
Vol 21 (2) ◽  
pp. 253-276 ◽  
Author(s):  
Charles Levi ◽  
Christian Partrat
Keyword(s):  
United States ◽  
Statistical Analysis ◽  
Negative Binomial ◽  
The United States ◽  
Normal Model ◽  
Chi Square ◽  
Expected Frequency ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Log Normal

AbstractA statistical analysis is performed on natural events which can produce important damages to insurers. The analysis is based on hurricanes which have been observed in the United States between 1954 et 1986.At first, independence between the number and the amount of the losses is examined. Different distributions (Poisson and negative binomial for frequency and exponential, Pareto and lognormal for severity) are tested. Along classical tests as chi-square, Kolmogorov-Smirnov and non parametric tests, a test with weights on the upper tail of the distribution is used: the Anderson – Darling test.Confidence intervals for the probability of occurrence of a claim and expected frequency for different potential levels of claims are derived. The Poisson Log-normal model gives a very good fit to the data.

scholarly journals Distribuições de probabilidade para séries históricas mensais de pressão atmosférica no município de Mossoró-RN

2016 ◽  
Vol 11 (2) ◽  
pp. 135
Author(s):  
Janilson Pinheiro de Assis ◽  
Roberto Pequeno de Sousa ◽  
Paulo César Ferreira Linhares ◽  
Thiago Alves Pimenta ◽  
Elcimar Lopes da Silva
Keyword(s):  
Atmospheric Pressure ◽  
Probability Distributions ◽  
Probability Density Distribution ◽  
Chi Square ◽  
Pearson Type ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Log Normal ◽  
Von Mises ◽  
Cramer Von Mises

<p>Objetivou-se verificar o ajuste de 12 séries históricas de pressão atmosférica mensal (milibar) no período de 1970 a2007, em Mossoró, RN, à sete modelos de distribuição densidade de probabilidade Normal, Log-Normal, Beta, Gama, Log-Pearson (Tipo III), Gumbel e Weibull, através dos testes Kolmogorov-Smirnov, Qui-Quadrado, Cramer Von-Mises, Anderson Darling e Kuiper a 10 % de probabilidade e utilizando-se o Logaritmo da Máxima Verossimilhança. Verificou-se a superioridade do ajustamento da distribuição de probabilidade Normal, quando comparada com as outras seis distribuições. No geral, os critérios de ajuste concordaram com a aceitação da hipótese H<sub>0</sub>, no entanto, deve-se salientar que o teste de Kolmogorov-Smirnov apresenta um nível de aprovação de uma distribuição sob teste muito elevado, gerando insegurança aos critérios do teste, porém, como neste estudo os dados são aproximadamente simétricos, esse é o mais recomendado.</p><p align="center"><strong><em>Probability distributions for historic series of monthly atmospheric pressure </em></strong><strong><em>in city</em></strong><strong><em> of Mossoró-RN</em></strong></p><p><strong>Abstract</strong><strong>: </strong>The aim of this study was to determine the set of 12 time series of monthly atmospheric pressure (millibars) in the period 1970-2007, in Natal, RN, the seven models of the probability density distribution Normal, Log-Normal, Beta, Gamma, Log -Pearson (Type III), Gumbel and Weibull, through the Kolmogorov-Smirnov tests, Chi-Square, Cramer-von Mises, Anderson Darling and Kuiper 10 probability and using the logarithm of the maximum likelihood. It is the superiority of adjusting the normal probability distribution compared to the other six distributions. Overall, the fit criteria agreed with the acceptance of the hypothesis, however, it should be noted that the Kolmogorov-Smirnov test shows a level of approval of a distribution under test very high, which creates some uncertainty to the criteria of test, but in this study as the data are roughly symmetrical it is the most recommended.</p>

scholarly journals Algoritmo para Determinação da Equação de Chuvas Intensas (Algorithm to Determine the Equation of Intense Rain)

2013 ◽  
Vol 6 (5) ◽  
pp. 1371 ◽  
Author(s):  
Simone Rosa da Silva ◽  
George Rodrigues De Sousa Araújo
Keyword(s):  
Extreme Values ◽  
Drainage System ◽  
Gumbel Distribution ◽  
Data Series ◽  
Extreme Precipitation Events ◽  
Kolmogorov Smirnov ◽  
Intensity Duration Frequency ◽  
Agile Process ◽  
Annual Means ◽  
The Cost

Estudos hidrológicos regionais são necessários em obras de engenharia relacionadas ao planejamento e aproveitamento dos recursos hídricos, pois eventos extremos de precipitações estão diretamente relacionados com os custos e a segurança das obras de aproveitamento hídrico, tais como: sistema de drenagem de águas pluviais, canais e bacias de detenção. O objetivo principal deste trabalho foi desenvolver e aplicar um algoritmo para determinação de parâmetros das equações IDF - Intensidade-Duração-Frequência, visando tornar o processo ágil a partir dos dados disponíveis de precipitação. Foi elaborada uma rotina computacional através da integração dos dados através de planilha eletrônica e software estatístico, que compreende regressões lineares múltiplas e processos gráficos. O algoritmo foi aplicado para obtenção da equação IDF para o município do Recife. Foi realizada a extrapolação de dados históricos de séries anuais através da distribuição de probabilidade de valores extremos de Gumbel, verificando-se sempre o ajuste dessa distribuição aos dados através do teste de Kolmogorov-Smirnov. A seguir, através da aplicação do algoritmo foram calculados os parâmetros da equação IDF para o respectivo posto pluviográfico, obtendo-se resultados satisfatórios. A B S T R A C T Regional hydrological studies are required on engineering works related to planning and use of water resources because of extreme precipitation events are directly related to the cost and safety of the works of water use, such as: drainage system rain water channels and basins detention. The main objective of this work is to develop and apply an algorithm for determining parameters of the equations IDF - Intensity-Duration-Frequency, designed to make the agile process from data available for precipitation. Was developed a computational routine by integrating data through spreadsheet and statistical software, which comprises multiple linear regressions and printing processes. The algorithm was applied to obtain the equation for the IDF city of Recife. We performed the extrapolation of historical data series of annual means of the probability distribution of extreme values of Gumbel, always checking the fit of this distribution to data using the Kolmogorov-Smirnov test. Then, by applying the algorithm parameters were calculated from the equation for the IDF pluviometric respective station, obtaining satisfactory results. Keywords: Rainfall intensity. Equations IDF. Gumbel Distribution.

scholarly journals Streamflow regionalization for the Mortes River Basin upstream from the Funil Hydropower Plant, MG

2020 ◽  
Vol 15 (3) ◽  
pp. 1 ◽  
Author(s):  
Jhones Da Silva Amorim ◽  
Rubens Junqueira ◽  
Vanessa Alves Mantovani ◽  
Marcelo Ribeiro Viola ◽  
Carlos Rogério de Mello ◽  
...  
Keyword(s):  
Resource Management ◽  
River Basin ◽  
Water Resource ◽  
Water Resource Management ◽  
Extreme Values ◽  
Kendall Test ◽  
Hydropower Plant ◽  
Coefficient Of Determination ◽  
Historical Series ◽  
Anderson Darling

 Maximum and minimum streamflow are fundamental for water resource management, especially for water rights. However, lack of monitoring and scarce streamflow data limit such studies. Streamflow regionalization is a useful tool to overcome these limitations. The study developed models for regionalization of the maximum and minimum reference streamflows for the Mortes River Basin (MRB) (Water Resources Planning and Management Unit - GD2), Southern Minas Gerais State. The study used long-term streamflow historical series provided by the Brazilian National Water Agency (ANA). Previous exploratory analysis was performed, and it was observed that the streamflow series are stationary according to the Mann-Kendall test. The estimation of the streamflow for different return periods (RP) was performed by fitting Probability Density Functions (PDFs) that were tested by the Anderson-Darling (AD) test. The Generalized Extreme Values (GEV) and Wakeby were the most appropriate PDFs for maximum and minimum streamflows, respectively. The streamflow models were fitted using a power regression procedure, considering the drainage area of the watersheds as inputs. The fittings reached the coefficient of determination (R2) greater than 0.90. Thus, the streamflow regionalization models demonstrated good performance and are a potential tool to be used for water resource management in the studied basin.

scholarly journals Estimating the Best-Fitted Probability Distribution for Monthly Maximum Temperature at the Sylhet Station in Bangladesh

2021 ◽  
Vol 2 (2) ◽  
pp. 60-67
Author(s):  
Rashidul Hasan Rashidul Hasan
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Probability Model ◽  
Temperature Data ◽  
Maximum Temperature ◽  
Chi Square ◽  
Goodness Of Fit Tests ◽  
Anderson Darling ◽  
Log Normal

The estimation of a suitable probability model depends mainly on the features of available temperature data at a particular place. As a result, existing probability distributions must be evaluated to establish an appropriate probability model that can deliver precise temperature estimation. The study intended to estimate the best-fitted probability model for the monthly maximum temperature at the Sylhet station in Bangladesh from January 2002 to December 2012 using several statistical analyses. Ten continuous probability distributions such as Exponential, Gamma, Log-Gamma, Beta, Normal, Log-Normal, Erlang, Power Function, Rayleigh, and Weibull distributions were fitted for these tasks using the maximum likelihood technique. To determine the model’s fit to the temperature data, several goodness-of-fit tests were applied, including the Kolmogorov-Smirnov test, Anderson-Darling test, and Chi-square test. The Beta distribution is found to be the best-fitted probability distribution based on the largest overall score derived from three specified goodness-of-fit tests for the monthly maximum temperature data at the Sylhet station.

scholarly journals PEMILIHAN DISTRIBUSI PROBABILITAS PADA ANALISA HUJAN DENGAN METODE GOODNESS OF FIT TEST

2016 ◽  
Vol 18 (2) ◽  
pp. 139-148
Author(s):  
Togani Cahyadi Upomo ◽  
Rini Kusumawardani
Keyword(s):  
Normal Distribution ◽  
Goodness Of Fit ◽  
Gumbel Distribution ◽  
Rainfall Event ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Pearson Iii Distribution

Rainfall event is a stochastic process, so to explain and analyze this processes the probability theory and frequency analysisare used. There are four types of probability distributions.They are normal, log normal, log Pearson III and Gumbel. To find the best probabilities distribution, it will used goodness of fit test. The tests consist of chi-square and smirnov-kolmogorov. Results of the chi-square test for normal distribution, log normal and log Pearson III was 0.200, while for the Gumbel distribution was 2.333. Results of Smirnov Kolmogorov test for normal distribution D = 0.1554, log-normal distribution D = 0.1103, log Pearson III distribution D = 0.1177 and Gumbel distribution D = 0.095. All of the distribution can be accepted with a confidence level of 95%, but the best distribution is log normal distribution.Kejadian hujan merupakan proses stokastik, sehingga untuk keperluan analisa dan menjelaskan proses stokastik tersebut digunakan teori probabilitas dan analisa frekuensi. Terdapat empat jenis distribusi probabilitas yaitu distribusi normal, log normal, log pearson III dan gumbel. Untuk mencari distribusi probabilitas terbaik maka akan digunakan pengujian metode goodness of fit test. Pengujian tersebut meliputi uji chi-kuadrat dan uji smirnov kolmogorov. Hasil pengujian chi kuadrat untuk distribusi normal, log normal dan log pearson III adalah 0.200, sedangkan untuk distribusi gumbel 2.333. Hasil pengujian smirnov kolmogorov untuk distribusi normal dengan nilai D = 0.1554, distribusi log normal dengan nilai D = 0.1103, distribusi log pearson III dengan nilai D = 0.1177 dan distribusi gumbel dengan nilai D = 0.095. Seluruh distribusi dapat diterima dengan tingkat kepercayaan 95%, tetapi distribusi terbaik adalah distribusi log normal.

scholarly journals Aplicação da Distribuição Nakagami na Análise de Dados de Precipitação

2019 ◽  
Vol 34 (1) ◽  
pp. 1-7
Author(s):  
Josmar Mazucheli ◽  
Isabele Picada Emanuelli
Keyword(s):  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Log Normal ◽  
Von Mises ◽  
Cramer Von Mises

Resumo Este trabalho teve como objetivo avaliar o desempenho da distribuição Nakagami na análise de séries de precipitação mensal, ao longo de vários anos, visando à seleção de uma distribuição útil para o planejamento e gestão de atividades dependentes dos índices de precipitação na Região Sul do Brasil. Para tanto, compara-se a mesma com cinco distribuições alternativas: Weibull, Gama, Log-Normal, Log-Logística e Inversa-Gaussiana. Foram utilizadas séries históricas de 33 estações meteorológicas observadas entre janeiro de 1970 a dezembro de 2014, totalizando 396 séries (33 estações × 12 meses). Para a escolha da distribuição, que forneceu o melhor ajuste, foram utilizados os valores dos critérios de informação de Akaike, de Kolmogorov-Smirnov, de Anderson-Darling e de Cramér-von Mises. Segundo estes critérios se encontrou que as distribuições Nakagami e Weibull foram selecionadas o maior número de vezes (Nakagami: 146 vezes e Weibull: 100 vezes). Embora a distribuição Nakagami não seja muito utilizada, na descrição de dados de precipitação, recomenda-se sua utilização na descrição do comportamento da pluviosidade mensal como alternativa para distribuições tradicionalmente utilizadas.

scholarly journals Determinação de equações de chuvas intensas para a encosta superior do nordeste do Rio Grande do Sul

2020 ◽  
Vol 42 ◽  
pp. e83
Author(s):  
Taison Anderson Bortolin ◽  
Clauber Corso ◽  
Ludmilson Abritta Mendes ◽  
Alan De Gois Barbosa ◽  
Vania Elisabete Schneider
Keyword(s):  
Rio Grande ◽  
Distribution Data ◽  
Rio Grande Do Sul ◽  
Chi Square ◽  
Significance Level ◽  
Gumbel’S Distribution ◽  
Kolmogorov Smirnov ◽  
Intensity Duration Frequency ◽  
Log Normal ◽  
The Relationship

The relationship intensity, duration and frequency is very important for the hydraulic project’s development, mainly in regions where there is no study updated data. This paper objective was to determine the intensity-duration-frequency curves at Rio Grande do Sul hillside, in order to provide tools for hydraulic structures design and hydrological studies in the region. For the return periods 2, 5, 10, 20, 25, 50 and 100 - year precipitation determination was used Gumbel’s and log-normal statistical distributions, using the Rain Relationship Duration Method for 20 rainfall stations. For Gumbel’s distribution data adherence verification, was used the Kolmogorov-Smirnov adhesion tests and Chi-Square adhesion, with, 5% significance level. The general IDF equation coefficients a, b, c and d were obtained through non-linear regression and the adjustment quality was measured by both determination coefficient and standard error. Different intense rainfall curves were obtained with the methodology applied, for the region, each one shows a good parameters adjustment, important tool for extreme precipitations estimating.

Sign in / Sign up

Export Citation Format

Share Document