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 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 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.

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

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 Favorable Estimators for Fitting Pareto Models: A Study Using Goodness-of-fit Measures with Actual Data

2003 ◽  
Vol 33 (2) ◽  
pp. 365-381 ◽  
Author(s):  
Vytaras Brazauskas ◽  
Robert Serfling
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Efficient Estimation ◽  
Small Samples ◽  
Robust Estimators ◽  
Trade Offs ◽  
Pareto Model ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

Several recent papers treated robust and efficient estimation of tail index parameters for (equivalent) Pareto and truncated exponential models, for large and small samples. New robust estimators of “generalized median” (GM) and “trimmed mean” (T) type were introduced and shown to provide more favorable trade-offs between efficiency and robustness than several well-established estimators, including those corresponding to methods of maximum likelihood, quantiles, and percentile matching. Here we investigate performance of the above mentioned estimators on real data and establish — via the use of goodness-of-fit measures — that favorable theoretical properties of the GM and T type estimators translate into an excellent practical performance. Further, we arrive at guidelines for Pareto model diagnostics, testing, and selection of particular robust estimators in practice. Model fits provided by the estimators are ranked and compared on the basis of Kolmogorov-Smirnov, Cramér-von Mises, and Anderson-Darling statistics.

scholarly journals Normalization of Showjumping Competition’s Results

2014 ◽  
Vol 14 (2) ◽  
pp. 391-403
Author(s):  
Zuzana Schubertová ◽  
Juraj Candrák
Keyword(s):  
Normal Distribution ◽  
Fixed Effects ◽  
Previous Model ◽  
Normal Score ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Well Data ◽  
Von Mises ◽  
Variable Ranking ◽  
Ks Test

Abstract The aim of this study was to verify the newly proposed transformation of penalty points and ranking of showjumping horses for the purpose of genetic evaluation. Genomic information in the transformation of input data was used as well. Data of showjumping competition Global Champions Tour was used. Profit of penalty points was transformed to normally distributed variable using Blom formula (height of obstacles and height of obstacles with single nucleotide polymorphism - SNP effect taken into account). Non-normal distribution was obtained. The rankings of sport horses in competitions were transformed using the Blom formula (height of obstacles taken into account) to normal distribution (tests of normality Kolmogorov-Smirnov (KS) test Pr>D, D 0.011, P>0.150, Cramer-von Mises (CM) test Pr>W-Sq, W-Sq 0.039, P>0.250, Anderson-Darling test (AD) Pr>A-Sq, A-Sq 0.638, P<0.097). Better distributed variable ranking transformed by Blom formula (height of obstacles and SNP effect taken into account) was obtained (KS test Pr>D, D 0.004, P>0.150, CM test Pr>W-Sq, W-Sq 0.004, P>0.250, AD test Pr>A-Sq, A-Sq 0.062, P>0.250). Model where all used fixed effects to equation were applied without any combination of the effects was tested, R2 0.54. Variable ranking was transformed to normal score by Blom formula (height of obstacles was taken into account). In the following model some effects were taken into account in the form of quadratic regression, R2 0.61. Variable ranking was transformed to normal score, the same as in previous model. In the last model we transformed variable ranking to normal score by Blom formula, taking into account height of obstacles and SNP effect. Same effects as in previous model were used, R2 0.60

Sign in / Sign up

Export Citation Format

Share Document