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.

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 Techniques of quality of adjustment of statistical models with evaluation of probability distributions using production data of laying quails

2021 ◽  
Vol 10 (11) ◽  
pp. e278101119317
Author(s):  
Antonio Augusto Carvas Sant’ Anna ◽  
Jacyara Lopes Pereira ◽  
Matheus Lima Corrêa Abreu ◽  
Adolpho Marlon Antoniol de Moura ◽  
Elon Souza Aniceto ◽  
...  
Keyword(s):  
Akaike Information Criterion ◽  
Probability Distributions ◽  
Information Criterion ◽  
Graphical Analysis ◽  
Cumulative Distribution ◽  
Continuous Data ◽  
Conditional Model ◽  
Anderson Darling ◽  
Von Mises

The goal of our study was to evaluate the quality of fit from different types of probability distributions for continuous data. For this, performance traits and quality of quail egg in the production of nutraceutical eggs were used as a continuous data source. The data were collected over 42 days, the experimental design was completely randomized with 7 treatments, 6 repetitions, with 252 animals allocated in 36 cages. The distributions for continuous data used were the exponential, gamma, gaussian, and lognormal. The R Open Source and SAS® University Edition software was used to perform the analysis. The graphical analysis of the traits was performed from the predicted versus observed values, Cumulative Distribution Function (CDF), and skewness-kurtosis. The fits were also evaluated by the Akaike information criterion (AIC), Bayesian information criterion (BIC), Conditional model of adjusted R-Square (), Conditional model of adjusted concordance correlation (), Kolmogorov-Smirnov test (KS), Cramer-von Mises test (CvM), Anderson-Darling test (AD), Watanabe-Akaike Information Criterion (WAIC) and Leave-one-out cross-validation (LOO). All the tests indicated the Gaussian distribution as the most suitable and they excluded the exponential distribution for all the evaluated characteristics.

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 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 WIND SPEED ANALYSIS AT IKEJA, NIGERIA USING THE CONVENTIONAL PROBABILITY DENSITY FUNCTIONS

2018 ◽  
Vol 24 (3) ◽  
Author(s):  
OLUSEYI OGUNSOLA ◽  
OGUNSOLA OSAGIEDE
Keyword(s):  
Likelihood Estimation ◽  
Information Criteria ◽  
Distribution Functions ◽  
Parameter Estimates ◽  
Energy Potential ◽  
Chi Square ◽  
Chi Square Test ◽  
Anderson Darling ◽  
Von Mises ◽  
Best Fit

<p>The wind energy potential at Ikeja (Lat. 6.35 °N; Long. 3.20 °E), Nigeria was statistically analyzed using three of the mostly utilized conventional Probability Distribution Functions (PDFs) in order to determine which of these distributions would give the best means of analysis for wind in this particular location. The best fit test for these PDFs were determined from Akaike Information Criteria, Bayesian Information Criteria, Kolmogorov-Smirnov test, Cramer-von Mises statistics, Anderson-Darling Statistic, Mean Square Error and Chi-Square Test using Maximum Likelihood Estimation and Method of Moments as parameter estimates. The Weibull distribution gave the best fit in this location.</p>

scholarly journals Modeling of probability in obtaining intensity-duration-frequency relationships of rainfall occurrence for Pelotas, RS, Brazil

2019 ◽  
Vol 23 (7) ◽  
pp. 499-505
Author(s):  
Viviane R. Dorneles ◽  
Rita de C. F. Damé ◽  
Claudia F. A. Teixeira-Gandra ◽  
Patrick M. Veber ◽  
Gustavo B. Klumb ◽  
...  
Keyword(s):  
Empirical Model ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Return Periods ◽  
Intense Rainfall ◽  
Maximum Rainfall ◽  
Rainfall Occurrence ◽  
Historical Series ◽  
Intensity Duration Frequency ◽  
Log Normal

ABSTRACT Based on historical series, for each locality, equations can characterize the relationship between intensity, duration and frequency of rainfall occurrence. The objective of this study was to present two equations that can describe the occurrence of intense rainfall in Pelotas, RS state, over the period 1982-2015. The two equations were denominated conventional and hybrid, depending on the probabilistic model used. Following the conventional methodology, the parameters of Normal, Log-Normal, Gumbel and Gamma probability distributions were adjusted by the maximum likelihood method for return periods of 2, 5, 10, 20, 25, 50 and 100 years. The maximum intensity values for the hybrid equation were obtained using the empirical model of Weibull, considering return periods of 2, 5, 10, 20 and 25 years. On the other hand, the same theoretical distributions used in the conventional equation were applied to return periods of 50 and 100 years. The Kolmogorov-Smirnov test was used to select the best fitting distribution for the data. In order to verify the information acquired through the Weibull empirical model in comparison to the theoretical distributions, the t-test was applied to the angular coefficients. Significant differences were not verified between the values of maximum rainfall intensities obtained using the two methodologies, for the pre-established durations and return periods. Thus, considering the maximum rainfall intensities values (durations of 5-1440 min) and return periods of 2-100 years in the municipality of Pelotas, RS, Brazil, both the hybrid and the conventional intense rainfall equations can be used.

scholarly journals Goodness-of-fit tests for the beta Gompertz distribution

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 69-81
Author(s):  
Hanaa Abu-Zinadah ◽  
Asmaa Binkhamis
Keyword(s):  
Goodness Of Fit ◽  
Real Data ◽  
Likelihood Method ◽  
Test Statistics ◽  
Gompertz Distribution ◽  
Goodness Of Fit Tests ◽  
Lilliefors Test ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This article studied the goodness-of-fit tests for the beta Gompertz distribution with four parameters based on a complete sample. The parameters were estimated by the maximum likelihood method. Critical values were found by Monte Carlo simulation for the modified Kolmogorov-Smirnov, Anderson-Darling, Cramer-von Mises, and Lilliefors test statistics. The power of these test statistics founded the optimal alternative distribution. Real data applications were used as examples for the goodness of fit tests.

scholarly journals The Topp-Leone Weibull Distribution: Its Properties and Application

2021 ◽  
pp. 381-401
Author(s):  
Diamond O. Tuoyo ◽  
Festus C. Opone ◽  
N. Ekhosuehi
Keyword(s):  
Weibull Distribution ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Information Criterion ◽  
Lifetime Data ◽  
Test Statistic ◽  
Data Set ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Von Mises

This paper presents a new generalization of the Topp-Leone distribution called the Topp-Leone Weibull Distribution (TLWD). Some of the mathematical properties of the proposed distribution are derived, and the maximum likelihood estimation method is adopted in estimating the parameters of the proposed distribution. An application of the proposed distribution alongside with some well-known distributions belonging to the Topp-Leone generated family of distributions, to a real lifetime data set reveals that the proposed distribution exhibits more flexibility in modeling lifetime data based on some comparison criteria such as maximized log-likelihood, Akaike Information Criterion [AIC=2k-2 log⁡(L) ], Kolmogorov-Smirnov test statistic (K-S) and Anderson Darling test statistic (A*) and Crammer-Von Mises test statistic (W*).

scholarly journals ASPECTOS ESPACIAIS DA EVAPOTRANSPIRAÇÃO COM O FOCO NO DIMENSIONAMENTO DE SISTEMAS DE IRRIGAÇÃO

Irriga ◽  
2019 ◽  
Vol 24 (4) ◽  
pp. 781-801
Author(s):  
Jefferson Vieira Jose ◽  
Lucas da C. Santos ◽  
Daniel S. Alves ◽  
Pablo R. Nitsche ◽  
Marcos V. Folegatti ◽  
...  
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Information Criterion ◽  
Global Solar Radiation ◽  
The State ◽  
Irrigation Systems ◽  
Daily Data ◽  
Crop Water Consumption ◽  
Log Normal ◽  
E Mail

ASPECTOS ESPACIAIS DA EVAPOTRANSPIRAÇÃO COM O FOCO NO DIMENSIONAMENTO DE SISTEMAS DE IRRIGAÇÃO     JEFFERSON VIEIRA JOSÉ1; LUCAS DA COSTA SANTOS2; DANIEL SOARES ALVES3; PABLO RICARDO NITSCHE4; MARCOS VINICIUS FOLEGATTI5 E WAGNER WOLFF6   1Centro multidisciplinar, UFAC, Campus Floresta, Rua Estrada da Canela Fina, KM 12 Gleba Formoso - São Francisco, CEP: 69895-000, Cruzeiro do Sul – AC, Brasil, e-email: [email protected] 2Departamento de Agronomia, UFVJM, Campus JK - Rodovia MGT 367, Km 583, nº5000 - Bairro Alto da Jacuba, CEP: 39100-000 – Diamantina – MG, Brasil,  e-email: [email protected] 3Departamento de Agrometeorologia. Instituição: Instituto Agronômico do Paraná - IAPAR. Endereço: Rodovia Celso Garcia Cid, km375, Bairro Ernani Moura Lima II, CEP: 86047-90, Londrina - PR, Brasil, e-mail: [email protected] 4Departamento de Agrometeorologia. Instituição: Instituto Agronômico do Paraná - IAPAR. Endereço: Rodovia Celso Garcia Cid, km375, Bairro Ernani Moura Lima II, CEP: 86047-90, Londrina - PR, Brasil, e-mail: [email protected] 5Departamento de Engenharia de Biossistemas, USP, ESALQ, Avenida Pádua Dias, 11, Bairro Agronomia, CEP: 13418-900, Piracicaba – SP, Brasil, e-mail: [email protected] 6Departamento de Engenharia de Biossistemas, USP, ESALQ, Avenida Pádua Dias, 11, Bairro: Agronomia, CEP: 13418-900, Piracicaba – SP, Brasil, e-mail: [email protected]                                                                                               1 RESUMO   Aspectos espaciais do consumo hídrico das culturas, com o foco no dimensionamento de sistemas de irrigação, é imprescindível para a racionalização do uso da água. Este trabalho objetivou analisar a distribuição de frequência da evapotranspiração de referência acumulada (EToac) no estado do Paraná por meio da espacialização dos parâmetros da distribuição de probabilidade, visando o dimensionamento de sistemas de irrigação. Dados diários de elementos meteorológicos (temperatura máxima, mínima e média; umidade relativa média; radiação solar global; insolação; velocidade do vento), entre os anos de 1980 a 2010, de 33 estações meteorológicas no estado do Paraná, foram utilizados na estimativa da evapotranspiração de referência (ETo) pelo método de Penman-Monteith. A ETo foi acumulada em períodos consecutivos de 5, 10, 20 e 30 dias e os seus valores máximos anuais foram avaliados e ajustados a nove distribuições de probabilidade (Log-normal, Weibull, Gamma, Cauchy, Normal, Logística, Birnbaum-Saunders, Gumbel e Gumbel-II). A distribuição de probabilidade de Gumbel II, verificada pelo Critério de Informação de Akaike, foi escolhida na geração de valores de EToac, nos diferentes níveis de probabilidade, por meio de mapas da distribuição dos parâmetros a e b para representar o estado do Paraná.   Keywords: Eventos extremos; geoestatística; Penman-Monteith; Paraná     JOSÉ, J. J.; SANTOS, L. C.; ALVES, S. S.; NITSCHE, P. R.; FOLEGATTI, M. V.; WOLFF, W. SPATIAL ASPECTS OF EVAPOTRANSPIRATION WITH FOCUS ON THE DESIGN OF IRRIGATION SYSTEMS     2 ABSTRACT   Spatial aspects of crop water consumption with focus on the design of irrigation systems is essential for rationalization of water use. This work aimed to analyze the frequency distribution of cumulative reference evapotranspiration (EToac) in the State of Paraná by means of spatialization of parameters of the probability distribution, aiming at the design of irrigation systems. Daily data of meteorological elements (maximum, minimum and average temperature, mean relative humidity, global solar radiation, insolation and wind speed) between the years of 1980 and 2010 of 33 meteorological stations in the State of Paraná were used to estimate evapotranspiration of (ETo) by the Penman-Monteith method. The ETo was accumulated in consecutive periods of 5, 10, 20 and 30 days and its annual maximum values were evaluated and adjusted to nine probability distributions (Log-normal, Weibull, Gamma, Cauchy, Normal, Logistics, Birnbaum-Saunders, Gumbel and Gumbel-II), the probability distribution of Gumbel II, verified by the Akaike Information Criterion, was chosen in the generation of EToac values, at the different levels of probability, by means of maps of distribution of the parameters a and b  to represent the State of Paraná.   Keywords: Extreme events, Gumbel, Geostatistics, Penman-Monteith, Parana

scholarly journals Fracture Statistics Using Three-Parameter and Two-Parameter Weibull Distributions for Fe-0.4C-1.5Cr-1.5Ni-0.8Mn-0.2Mo Structural Sintered Steel

2016 ◽  
Vol 61 (3) ◽  
pp. 1547-1554 ◽  
Author(s):  
Ch. Fiał ◽  
A. Ciaś ◽  
A. Czarski ◽  
M. Sułowski
Keyword(s):  
Maximum Likelihood Method ◽  
Probability Distributions ◽  
Likelihood Method ◽  
Sufficient Evidence ◽  
Parameter Distribution ◽  
Sintered Steel ◽  
Weibull Statistics ◽  
Sintered Steels ◽  
Anderson Darling ◽  
Two Parameter

Abstract A statistical analysis is presented of tensile and bending strengths of a porous sintered structural steel which exhibits non-linear, quasi-brittle, behaviour. It is the result of existing natural flaws (pores and oxide inclusions) and of the formation of fresh flaws when stress is applied. The analysis is by two- and three-parameter Weibull statistics. Weibull modulus, a measure of reliability, was estimated by the maximum likelihood method for specimen populations < 30. Probability distributions were compared on the basis of goodness to fit using the Anderson-Darling tests. The use of the two-parameter Weibull distribution for strength data of quasi-brittle sintered steels is questioned, because there is sufficient evidence that the 3-parameter distribution fits the data better.

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