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 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.

Analysis of Magnitude and Frequency of Floods in the Damanganga Basin: Western India

2021 ◽  
Vol 5 (1) ◽  
pp. 1-11
Author(s):  
Vitthal Anwat ◽  
Pramodkumar Hire ◽  
Uttam Pawar ◽  
Rajendra Gunjal
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Western India ◽  
Type I ◽  
Return Periods ◽  
Pearson Type ◽  
Kolmogorov Smirnov ◽  
Anderson Darling

Flood Frequency Analysis (FFA) method was introduced by Fuller in 1914 to understand the magnitude and frequency of floods. The present study is carried out using the two most widely accepted probability distributions for FFA in the world namely, Gumbel Extreme Value type I (GEVI) and Log Pearson type III (LP-III). The Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) methods were used to select the most suitable probability distribution at sites in the Damanganga Basin. Moreover, discharges were estimated for various return periods using GEVI and LP-III. The recurrence interval of the largest peak flood on record (Qmax) is 107 years (at Nanipalsan) and 146 years (at Ozarkhed) as per LP-III. Flood Frequency Curves (FFC) specifies that LP-III is the best-fitted probability distribution for FFA of the Damanganga Basin. Therefore, estimated discharges and return periods by LP-III probability distribution are more reliable and can be used for designing hydraulic structures.

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 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 Probabilistic Modeling of Monthly Temperature Historical Series in Mossoró, Northeastern Brazil

2018 ◽  
Vol 10 (12) ◽  
pp. 534
Author(s):  
Janilson Pinheiro de Assis ◽  
Roberto Pequeno de Sousa ◽  
Ben Deivide de Oliveira Batista ◽  
Paulo César Ferreira Linhares ◽  
Eudes de Almeida Cardoso ◽  
...  
Keyword(s):  
Goodness Of Fit ◽  
Northeastern Brazil ◽  
Chi Square ◽  
Empirical Distributions ◽  
Monthly Temperature ◽  
Small Series ◽  
Pearson Type ◽  
Historical Series ◽  
Kolmogorov Smirnov ◽  
Von Mises

We fitted the following seven distribution probabilities to the data of monthly average temperature in Mossor&oacute;, northeastern Brazil: Normal, Log-Normal, Beta, Gamma, Log-Pearson (Type III), Gumbel, and Weibull. To assess the goodness of fit the empirical distributions to the theoretical distribution, we applied the tests of Kolmogorov-Smirnov, Chi-square, Cramer-von Mises, Anderson-Darling, Kuiper, and Logarithm of Maximum Likelihood, at 10% of probability. The temperature series were obtained from 1970 to 2007. The Normal distribution provided the best fit to the historical series of average monthly temperature. Although the Kolmogorov-Smirnov test showed a very high level of approval, which generated some uncertainty regarding the test criteria, it is the more recommended to studies with approximately symmetric data and small series.

scholarly journals Aplicación de un modelo de calidad de agua y definición de criterios para el monitoreo de un fertilizante en una cuenca rural

2004 ◽  
Vol 11 (4) ◽  
pp. 411
Author(s):  
Mónica E. Gelmi ◽  
Rafael Santiago Seoane
Keyword(s):  
Water Quality ◽  
Water Resources ◽  
Buenos Aires ◽  
Kolmogorov Smirnov ◽  
Log Normal ◽  
Von Mises ◽  
Cramer Von Mises

El objetivo de este trabajo consiste en aplicar el modelo de calidad de agua denominado Simulator Water Resources in Rural Basins - Water Quality (SWRRB-WQ) asociado a un modelo de generación de variables hidrometeorológicas, Richardson (1981), para estimar la masa de fertilizante nitrogenado transportado por el escurrimiento superficial en una subcuenca del arroyo Tapalqué (Provincia de Buenos Aires, Argentina). Se diseña un plan de experimentos con el propósito de definir las principales características de un programa de muestreo para estudiar la carga de nitratos que se encuentra asociada con la aplicación del fertilizante nitrogenado en una subcuenca que tiene una superficie sembrada de aproximadamente 202 km2. Con el propósito de simular la altura de la precipitación diaria, variable de entrada del modelo hidrológico y de calidad deagua, se propone seleccionar el modelo estocástico más adecuado entre las funciones de densidad de probabilidades: Gamma,Log-Normal II, Log-Normal III y Exponencial, a partir de la aplicación de los estadísticos de Kolmogorov-Smirnov y de Cramer-von Mises. Un objetivo importante es estimar la carga de nitratos en la sección del arroyo Tapalqué correspondiente al cierre de la subcuenca motivo de estudio para distintos escenarios de aplicación del fertilizante nitrogenado en distinta magnitud asociado a diferentes trazas sintéticas de variables hidrometeorológicas a partir del modelo de generación de variables hidrometeorológicas, Richardson (1981). A partir de las simulaciones realizadas, se estima la función de correlación cruzada entre la altura de la precipitación y la carga de nitratos contenida en el escurrimiento que permite definir el tiempo medio de retardo entre ambas variables. Este resultado es importante ya que define el período de tiempo posterior a la ocurrencia del evento de precipitación, para el cual sería importante intensificar los muestreos en la sección del arroyo Tapalqué correspondiente al cierre de la subcuenca en estudio.

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 Evaluation of probability distributions in the analysis of minimum temperature series in Manaus – AM

2021 ◽  
Vol 10 (3) ◽  
pp. e46210313616
Author(s):  
Yana Miranda Borges ◽  
Breno Gabriel da Silva ◽  
Brian Alvarez Ribeiro de Melo ◽  
Robério Rebouças da Silva
Keyword(s):  
Probability Distributions ◽  
Information Criterion ◽  
Biological Species ◽  
Temperature Series ◽  
Likelihood Method ◽  
Historical Temperature ◽  
Anderson Darling ◽  
Log Normal ◽  
Von Mises ◽  
Best Fit

The relevance in studying climatological phenomena is based on the influence that variables of this nature exert on the world. Among the most observed variables, temperature stands out, whose effect of its variation may cause significant impacts, such as the proliferation of biological species, agricultural production, population health, etc. Probability distributions have been studied to verify the best fit to describe and/or predict the behavior of climate variables and, in this context, the present study evaluated, among six probability distributions, the best fit to describe a historical temperature series. minimum monthly mean. The series used in this study encompass a period of 38 years (1980 to 2018) separated by month from the weather station of the Manaus - AM station (OMM: 82331) obtained from INMET, totaling 459 observations. Difference-Sign and Turning Point tests were used to verify data independence and the maximum likelihood method to estimate the parameters. Kolmogorov-Smirnov, Anderson-Darling, Cramér-von Mises, Akaike Information Criterion and quantile-quantile plots were used to select the best fit distribution. Log-Normal, Gama, Weibull, Gumbel type II, Benini and Rice distributions were evaluated, with the best performing Rice, Log-Normal and Gumbel II distributions being highlighted.

Fitting The Statistical Distributions To The Daily Rainfall Amount In Peninsular Malaysia

2012 ◽  
Author(s):  
Suhaila Jamaludin ◽  
Abdul Aziz Jemain
Keyword(s):  
Goodness Of Fit ◽  
Daily Rainfall ◽  
Peninsular Malaysia ◽  
Rainfall Amount ◽  
Likelihood Method ◽  
Goodness Of Fit Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises ◽  
Cramer Von Mises

Data hujan harian dibahagikan kepada empat jenis rentetan hujan (jenis 1, 2, 3 dan 4). Taburan Gamma, Weibull, Kappa dan Gabungan Eksponen ialah empat taburan statistik yang diuji dalam memadankan data jumlah hujan harian di Semenanjung Malaysia. Parameter bagi setiap taburan dianggar dengan menggunakan kaedah kebolehjadian maksimum. Model dipilih berdasarkan nilai ralat yang minimum terhasil dari tujuh ujian kesesuaian model iaitu median bagi perbezaan nilai mutlak antara taburan empirik dengan taburan yang diuji, statistik fungsi empirik iaitu Kolmogorov-Smirnov D, Anderson Darling A2 dan Cramer-von-Mises W2 serta kaedah baru statistik fungsi empirik yang berasaskan kepada ujian nisbah kebolehjadian. Berdasarkan nilai ujian kesesuaian model, didapati taburan Gabungan Eksponen adalah yang paling sesuai dalam memadankan data jumlah hujan harian di Semenanjung Malaysia. Kata kunci: Jumlah hujan harian, ujian kesesuaian model, gabungan eksponen Daily rainfall data have been classified according to four rain types of sequence of wet days (Type 1, 2, 3 and 4). The Gamma, Weibull, Kappa and Mixed Exponential are the four distributions that have been tested to fit daily rainfall amount in Peninsular Malaysia. Parameter for each distribution were estimated using the maximum likelihood method. The selected model is chosen based on the minimum error produced by seven goodness-of-fit (GOF) tests namely the medium of absolute difference (MAD) between the empirical and hypothesized distributions, the traditional Empirical Distribution Function (EDF) Statistics which include Kolmogorov-Smirnov statistic D, Anderson Darling statistic A2 and Cramer-von-Mises statistic W2 and the new method of EDF Statistic based on likelihood ratio statistic. Based on these goodness-of-fit test, the Mixed Exponential is found to be the most approriate distribution for describing the daily rainfall amount in Peninsular Malaysia. Key words: Dairy rainfall amount, goodness–of–fit test, mixed exponential

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