ADEQUAÇÃO DE MODELOS PROBABILÍSTICOS À EVAPOTRANSPIRAÇÃO DE REFERÊNCIA NO SUBMÉDIO DO VALE DO RIO SÃO FRANCISCO

ADEQUAÇÃO DE MODELOS PROBABILÍSTICOS À EVAPOTRANSPIRAÇÃO DE REFERÊNCIA NO SUBMÉDIO DO VALE DO RIO SÃO FRANCISCO EDGO JACKSON PINTO SANTIAGO1; FRANK GOMES-SILVA 1; ANTONIO SAMUEL ALVES DA SILVA1; JOSÉ RAMON BARROS CANTALICE1; MOACYR CUNHA FILHO1 E JOSÉ DOMINGOS ALBUQUERQUE AGUIAR1 1 Departamento de Estatística e Informática-DEINFO, Programa de Pós-Graduação em Biometria e Estatística Aplicada-PPGBEA, Universidade Federal Rural de Pernambuco-UFRPE, Rua Dom Manoel de Medeiros s/n, Dois Irmãos, CEP: 52.171.900, Recife, Pernambuco, Brasil. [email protected], [email protected], [email protected], [email protected], [email protected], [email protected]. 1 RESUMO A evapotranspiração consiste no processo de perda de água do solo, da planta, e é fundamental para produção vegetal, constituindo uma das principais variáveis agrometeorológicas. Apesar disso, são escassos trabalhos que relacionam adequabilidade de distribuições de probabilidade a dados de evapotranspiração. O objetivo desse trabalho foi testar a aderência de diferentes distribuições de probabilidade à dados de evapotranspiração de referência, selecionando as mais adequadas para este fim. Esse estudo foi realizado com dados de evapotranspiração de referência obtidos pelas estações meteorológicas da Universidade Federal do Vale do São Francisco (UNIVASF) em Petrolina, PE e Juazeiro, BA. Foram ajustadas as distribuições Gama, Weibull, Log-Normal, Beta, Exponencial, Log-Logística e Log-Logística Exponenciada. Os maiores p-valores foram obtidos para as distribuições Log-Logística e Log-Logística Exponenciada, possivelmente devido à leve assimetria positiva destas aos dados de evapotranspiração. Pelo teste da razão de verossimilhanças, a distribuição Log-Logística Exponenciada adequou-se mais aos meses de janeiro, agosto e dezembro em Juazeiro e Petrolina, somando-se a esta última o mês de novembro. As distribuições Log-Logística e Log-Logística Exponenciada foram as mais adequadas para modelar a evapotranspiração. A partir dessas distribuições, foram estimados valores de evapotranspiração para diferentes níveis de probabilidade, sendo janeiro o mês com maior demanda hídrica provável. Palavras-chave: transpiração, evaporação, demanda hídrica, distribuição log-logística, irrigação. SANTIAGO, E. J. P.; GOMES-SILVA, F.; SILVA, A. S. A.; CANTALICE, J. R. B.; CUNHA FILHO, M.; AGUIAR, J. D. A. ADJUSTMENT OF PROBABILISTIC MODELS TO THE REFERENCE EVAPOTRANSPIRATION IN THE SUB-MEDIUM OF SÃO FRANCISCO RIVER VALLEY 2 ABSTRACT Evapotranspiration is the process of water loss from soil and plant surfaces, and it is essential for plant production, constituting one of the main agrometeorological variables. Nevertheless, there are few studies that relate the adequacy of probability distributions to evapotranspiration data. The objective of this work was to test the adherence of different probability distributions to reference evapotranspiration data by selecting the most suitable ones for this purpose. This study was carried out with daily evapotranspiration reference data obtained by the meteorological stations of the Federal University of Vale of São Francisco (UNIVASF) in Petrolina, PE and Juazeiro, BA. The Gamma, Weibull, Log-Normal, Beta, Exponential, Log-Logistics and Exponentiated Log-Logistics distribution were adjusted. The highest p-values were obtained for the Log-Logistics and Exponentiated Log-Logistics distributions. The highest p-values were obtained for the Log-Logistics and Exponentiated Log-Logistics distributions, possibly due to the slight positive asymmetry of those to the evapotranspiration data. By testing the likelihood ratio, the Exponentiated Log-Logistics distribution was more suitable for the months of January, August and December in Juazeiro and Petrolina, adding to the latter the month of November. The Log-Logistics and Exponentiated Log-Logistics distributions were the most suitable to model evapotranspiration. From these distributions, evapotranspiration values were estimated for different levels of probability, with January being the month with the highest probable water demand. Keywords: transpiration, evaporation, water demand, log-logistics distribution, irrigation.

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Standard distributions in R.

Practical R for biologists: an introduction ◽

10.1079/9781789245349.0030 ◽

2021 ◽

pp. 335-347

Author(s):

Donald L. J. Quicke ◽

Buntika A. Butcher ◽

Rachel A. Kruft Welton

Keyword(s):

Programming Language ◽

Negative Binomial ◽

Probability Distributions ◽

Test Statistics ◽

P Values ◽

Chi Squared ◽

Student’S T ◽

Log Normal

Abstract There are a number of in-built probability distributions, including uniform, binomial, negative binomial, normal, log-normal, logistic, exponential, Chisquared, Poisson, gamma, Fisher's F, Student's t, Weibull and others. These are used to generate p-values from test statistics, to generate random values from a distribution or to generate expected distributions. This chapter deals with standard distributions in R (a programming language that has a huge range of inbuilt statistical and graphical functions), focusing on the normal, Student's t, lognormal, logistic, Poisson, gamma, and the Chi-squared.

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Standard distributions in R.

Practical R for biologists: an introduction ◽

10.1079/9781789245349.0335 ◽

2021 ◽

pp. 335-347

Author(s):

Donald L. J. Quicke ◽

Buntika A. Butcher ◽

Rachel A. Kruft Welton

Keyword(s):

Programming Language ◽

Negative Binomial ◽

Probability Distributions ◽

Test Statistics ◽

P Values ◽

Chi Squared ◽

Student’S T ◽

Log Normal

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Probability Distributions (Normal and Log-Normal)

Engineering Modelling and Analysis ◽

10.1201/9781315274867-35 ◽

2018 ◽

pp. 257-264

Keyword(s):

Probability Distributions ◽

Log Normal

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INFLUÊNCIA DA FORMA DE OBTENÇÃO DO SALDO DE RADIAÇÃO NA COMPARAÇÃO DE MÉTODOS DE ESTIMATIVA DA EVAPOTRANSPIRAÇÃO DE REFERÊNCIA

Irriga ◽

10.15809/irriga.2005v10n3p215-228 ◽

2005 ◽

Vol 10 (3) ◽

pp. 215-228 ◽

Cited By ~ 1

Author(s):

José Eduardo Pitelli Turco ◽

Manoel Teixeira de Faria ◽

Edemo João Fernandes

Keyword(s):

Standard Method ◽

Reference Evapotranspiration ◽

Weather Station ◽

State University ◽

Net Radiation ◽

Paulo State ◽

Class A ◽

Engineering Department ◽

Daily Evapotranspiration ◽

Class A Pan

INFLUÊNCIA DA FORMA DE OBTENÇÃO DO SALDO DE RADIAÇÃO NA COMPARAÇÃO DE MÉTODOS DE ESTIMATIVA DA EVAPOTRANSPIRAÇÃO DE REFERÊNCIA José Eduardo Pitelli Turco; Manoel Teixeira de Faria; Edemo João FernandesDepartamento de Engenharia Rural, Faculdade de Ciências Agrárias e Veterinárias, Universidade Estadual Paulista, Câmpus de Jaboticabal, Jaboticabal , SP, [email protected] 1 RESUMO Uma maneira freqüentemente utilizada para verificar a eficiência de métodos de estimativa da evapotranspiração de referência (ETo) em diferentes situações e locais é por meio de comparação com um método padrão. Porém, a utilização de diferentes métodos para a obtenção do saldo de radiação, empregado na estimativa da evapotranspiração, pode conduzir a resultados distintos. O objetivo desse trabalho foi avaliar a influência do método de obtenção do saldo de radiação na comparação de quatro métodos (FAO-Tanque Classe A, FAO-Radiação Solar, Makkink e Hargreaves-Samani) com o método padrão recomendado pela FAO (Penman-Monteith). A pesquisa foi desenvolvida em área experimental do Departamento de Engenharia Rural da FCAV/UNESP, Campus de Jaboticabal, SP, onde foi instalada uma estação meteorológica automatizada e um Tanque Classe A. Por intermédio de um sistema de aquisição de dados foram obtidas medidas da radiação solar global, saldo de radiação, temperatura do ar, umidade relativa do ar e velocidade do vento. Os resultados indicam que as formas de obtenção do saldo de radiação podem alterar a estimativa da evapotranspiração diária obtida pelo método de Penman-Monteith. UNITERMOS: estação meteorológica automatizada, radiação solar, Penman-Monteith TURCO, J. E. P.; FARIA, M. T. de; FERNANDES E. J. INFLUENCE OF NET RADIATION OBTENTION METHOD COMPARED TO THE REFERENCE EVAPOTRANSPIRATION ESTIMATE METHODS 2 ABSTRACT One way to verify the efficiency of evapotranspiration reference (ETo) estimate methods in different conditions is through the comparison to a standard method. However the utilization of several methods to obtain the net radiation using evapotranspiration reference estimate, can end up in different results. The purpose of this paper was to evaluate the influence of the net radiation obtention method compared to four methods (FAO – Class A pan, FAO – Radiation, Makkink and Hargreaves-Samani) to the Penman-Montheith method which is considered a standard method by FAO. The research was carried out at an experimental area of the Rural Engineering Department of FCAV/São Paulo State University, Jaboticabal, SP, Brazil. Global net radiation, air temperature, air relative humidity, and wind speed were obtained using an automated weather station equipped with sensors. The results showed that the net radiation obtaintion methods can alter the daily evapotranspiration estimate obtained by the Penman-Montheith method. KEYWORDS: automated weather station, solar radiation, Penman-Monteith

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

Journal of Mathematics and Statistics Studies ◽

10.32996/jmss.2021.2.2.7 ◽

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.

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Evaluating probabilistic programming and fast variational Bayesian inference in phylogenetics

10.1101/702944 ◽

2019 ◽

Cited By ~ 1

Author(s):

Mathieu Fourment ◽

Aaron E. Darling

Keyword(s):

Probabilistic Models ◽

Probability Distributions ◽

Mean Field ◽

Black Box ◽

Variational Inference ◽

Machine Learning Techniques ◽

Mcmc Methods ◽

Substitution Model ◽

Probabilistic Programming ◽

Phylogenetic Models

AbstractRecent advances in statistical machine learning techniques have led to the creation of probabilistic programming frameworks. These frameworks enable probabilistic models to be rapidly prototyped and fit to data using scalable approximation methods such as variational inference. In this work, we explore the use of the Stan language for probabilistic programming in application to phylogenetic models. We show that many commonly used phylogenetic models including the general time reversible (GTR) substitution model, rate heterogeneity among sites, and a range of coalescent models can be implemented using a probabilistic programming language. The posterior probability distributions obtained via the black box variational inference engine in Stan were compared to those obtained with reference implementations of Markov chain Monte Carlo (MCMC) for phylogenetic inference. We find that black box variational inference in Stan is less accurate than MCMC methods for phylogenetic models, but requires far less compute time. Finally, we evaluate a custom implementation of mean-field variational inference on the Jukes-Cantor substitution model and show that a specialized implementation of variational inference can be two orders of magnitude faster and more accurate than a general purpose probabilistic implementation.

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Mathematics and Statistics in Anesthesiology

10.2310/anes.18276 ◽

2018 ◽

Author(s):

Daniel Mortlock

Keyword(s):

Probability Theory ◽

Data Analysis ◽

Survey Design ◽

Probability Distributions ◽

Statistical Tests ◽

Real World Data ◽

Mathematical Functions ◽

P Values ◽

Bayesian Data Analysis ◽

Probability And Statistics

Mathematics is the language of quantitative science, and probability and statistics are the extension of classical logic to real world data analysis and experimental design. The basics of mathematical functions and probability theory are summarized here, providing the tools for statistical modeling and assessment of experimental results. There is a focus on the Bayesian approach to such problems (ie, Bayesian data analysis); therefore, the basic laws of probability are stated, along with several standard probability distributions (eg, binomial, Poisson, Gaussian). A number of standard classical tests (eg, p values, the t-test) are also defined and, to the degree possible, linked to the underlying principles of probability theory. This review contains 5 figures, 1 table, and 15 references. Keywords: Bayesian data analysis, mathematical models, power analysis, probability, p values, statistical tests, statistics, survey design

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Reliability Against Drifting Ice—An Adjunct to Monte Carlo Simulation

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2919928 ◽

1991 ◽

Vol 113 (3) ◽

pp. 253-259

Author(s):

A. B. Dunwoody

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Normal Family ◽

Probability Distributions ◽

Load Model ◽

Ice Load ◽

Ice Loads ◽

Drifting Ice ◽

Log Normal ◽

Monte Carlo Simulation Program

A method is presented for the calculation of the reliability of a structure against drifting ice subject to restrictions on the form of the ice load model and on the form of the probability distributions of the ice feature characteristics. The ice load model must have the form that the ice load is proportional to the product of the characteristics of the impacting ice feature raised to individual powers. Results from a Monte Carlo simulation program are presented to demonstrate that the ice loads for a number of useful ice interaction scenarios can be modeled by an equation of this form. The probability distributions of the ice feature characteristics must be from the log-normal family. A realistic example using publicly available ice data and ice load model is presented.

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The Nested_fit Data Analysis Program

Proceedings ◽

10.3390/proceedings2019033014 ◽

2019 ◽

Vol 33 (1) ◽

pp. 14 ◽

Cited By ~ 1

Author(s):

Martino Trassinelli

Keyword(s):

Data Analysis ◽

Probability Distributions ◽

Analysis Program ◽

Large Database ◽

Data Set ◽

Lawn Mower ◽

Bayesian Data Analysis ◽

Bayesian Evidence ◽

Spectral Profiles ◽

Log Normal

We present here Nested_fit, a Bayesian data analysis code developed for investigations of atomic spectra and other physical data. It is based on the nested sampling algorithm with the implementation of an upgraded lawn mower robot method for finding new live points. For a given data set and a chosen model, the program provides the Bayesian evidence, for the comparison of different hypotheses/models, and the different parameter probability distributions. A large database of spectral profiles is already available (Gaussian, Lorentz, Voigt, Log-normal, etc.) and additional ones can easily added. It is written in Fortran, for an optimized parallel computation, and it is accompanied by a Python library for the results visualization.

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Probabilistic Models Applicable to the Short-Term Extreme Response Analysis of Jack-Up Platforms

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.1600470 ◽

2003 ◽

Vol 125 (4) ◽

pp. 249-263 ◽

Cited By ~ 1

Author(s):

M. J. Cassidy ◽

G. T. Houlsby ◽

R. Eatock Taylor

Keyword(s):

Probabilistic Models ◽

Probability Distributions ◽

Response Analysis ◽

Wave Loading ◽

Physical Processes ◽

Short Term ◽

Analysis Techniques ◽

Extreme Response ◽

Increasing Demand ◽

Jack Up

There is a steadily increasing demand for the use of jack-up units in deeper water and harsher conditions. Confidence in their use in these environments requires jack-up analysis techniques to reflect accurately the physical processes occurring. However, nearly all analyses are deterministic in nature and do not account for the inherent variability in governing parameters and models. In this paper, probabilistic models are used to develop an understanding of the response behavior of jack-ups, with particular emphasis placed on the extreme deck displacement due to a short-term event. Variables within the structural, foundation and wave loading models are assigned probability distributions and their influence on the response statistics is quantified using a response surface methodology.

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