scholarly journals EVALUATION OF THE BEST-FIT PROBABILITY OF DISTRIBUTION AND RETURN PERIODS OF RIVER DISCHARGE PEAKS. CASE STUDY: AWETU RIVER, JIMMA, ETHIOPIA

2019 ◽  
Vol 4 (4) ◽  
pp. 361-368 ◽  
Author(s):  
Tolera Abdisa Feyissa ◽  
Nasir Gebi Tukura
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Peak Discharge ◽  
Environmental Damage ◽  
Return Periods ◽  
Chi Squared ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Log Normal ◽  
Best Fit

The identification of the best distribution function is essential to estimate a river peak discharge or magnitude of river floods for management of watershed and ecosystems. However, inadequate estimation of the river peak discharge and floods magnitude may decrease the efficiency of water-resources management, resulting in soil erosion, landslides, environmental damage and ecosystem degradation. To overcome this problem in hydrology, different methods have been employed, applying a probability distribution.In this study to determine the suitable probability of distribution for estimating the annual discharge series with different return periods, the annual mean and peak discharges of the Awetu River (Jimma, Ethiopia) over a 24 years’ time period have been collected and used. After the homogeneity and consistency test, data were analyzed to predict extreme values and were applied in seven different probability distribution functions by using L-moment and easy fit methods. Then, three goodness of fit tests, Anderson-Darling (AD), Kolmogorov-Smirnov (KS), and Chi-Squared (x2) tests, were used to select the best probability distribution function for the study area. The obtained results indicate that, Log-normal distribution function is the best-fit distribution to estimate the peak discharge recurrence of the Awetu River. The 5-year, 10-year, 25-year, 50-year, 100-year and 1000-year return periods of discharge were calculated for this river. The results of this study are useful for the development of more accurate models of flooding inundation and hazard analysis. AVALIAÇÃO DA MELHOR PROBABILIDADE DE AJUSTE DE DISTRIBUIÇÃO E PERÍODOS DE RETORNO DOS PICOS DE DESCARGA FLUVIAL. ESTUDO DE CASO: AWETU RIVER, JIMMA, ETIÓPIAResumoAvaliação da melhor função de probabilidade de distribuição e de períodos de retorno de picos de descarga de rio. Estudo de caso: Rio Awetu, Jimma, Etiópia. A identificação da melhor função de distribuição é essencial para estimar um pico de descarga de rios ou a magnitude das inundações de bacias hidrográficas e ecossistemas, tendo em vista a gestão dos sistemas hídricos e dos ecossistemas. Entretanto, uma estimativa inadequada da magnitude do pico de vazão e inundações do rio pode diminuir a eficiência do gerenciamento dos recursos hídricos, resultando em erosão do solo, deslizamentos de terra, danos ambientais e degradação do ecossistema. Para superar esse problema na hidrologia, diferentes métodos foram empregados, aplicando funções de probabilidade de distribuição e retorno.Neste estudo, para determinar a probabilidade adequada de distribuição e para estimar séries de descarga anuais com diferentes períodos de retorno, foram usados dados de médias anuais de picos de descarga do Rio Awetu (Jimma, Etiópia) durante um período de 24 anos. Após o teste de homogeneidade e consistência, os dados foram analisados para prever valores extremos e foram aplicados a sete funções diferentes de probabilidade de distribuição, usando o momento L e métodos de ajuste fácil. Em seguida foram utilizados, três testes de qualidade de ajuste, Anderson-Darling (AD), Kolmogorov-Smirnov (KS), and Chi-Squared (x2), para selecionar a melhor função de probabilidade de distribuição para a área de estudo. Os resultados obtidos indicam que, a função de distribuição log-normal é a que mais se adequa para estimar a recorrência de picos de descarga do Rio Awetu. Os períodos de retorno de descarga de 5 anos, 10 anos, 25 anos, 50 anos, 100 anos e 1000 anos foram calculados para este rio. Os resultados deste estudo são úteis para o desenvolvimento de modelos mais precisos de inundação e análise de risco.Palavras-chave: Descarga de Rio. Qualidade de ajuste. Log Pearson Tipo III. Distribuição de probabilidade. 

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 Frequency analysis of low flows in intermittent and non-intermittent rivers from hydrological basins in Turkey

2018 ◽  
Vol 19 (1) ◽  
pp. 30-39 ◽  
Author(s):  
Ebru Eris ◽  
Hafzullah Aksoy ◽  
Bihrat Onoz ◽  
Mahmut Cetin ◽  
Mehmet Ishak Yuce ◽  
...  
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Distribution Functions ◽  
Low Flow ◽  
Probability Distribution Functions ◽  
Low Flows ◽  
Intermittent Rivers ◽  
Log Normal ◽  
Best Fit

Abstract This study attempts to find out the best-fit probability distribution function to low flows using the up-to-date data of intermittent and non-intermittent rivers in four hydrological basins from different regions in Turkey. Frequency analysis of D = 1-, 7-, 14-, 30-, 90- and 273-day low flows calculated from the daily flow time series of each stream gauge was performed. Weibull (W2), Gamma (G2), Generalized Extreme Value (GEV) and Log-Normal (LN2) are selected among the 2-parameter probability distribution functions together with the Weibull (W3), Gamma (G3) and Log-Normal (LN3) from the 3-parameter probability distribution function family. Selected probability distribution functions are checked for their suitability to fit each D-day low flow sequence. LN3 mostly conforms to low flows by being the best-fit among the selected probability distribution functions in three out of four hydrological basins while W3 fits low flows in one basin. With the use of the best-fit probability distribution function, the low flow-duration-frequency curves are determined, which have the ability to provide the end-users with any D-day low flow discharge of any given return period.

Prediction of Haemoglobin Level by Some Probability Distribution

2020 ◽  
Vol 9 (1) ◽  
pp. 84-88
Author(s):  
Govinda Prasad Dhungana ◽  
Laxmi Prasad Sapkota
Keyword(s):  
Probability Distribution ◽  
Normal Distribution ◽  
Goodness Of Fit ◽  
Continuous Variable ◽  
Hemoglobin Level ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Two Parameters ◽  
Best Fit

 Hemoglobin level is a continuous variable. So, it follows some theoretical probability distribution Normal, Log-normal, Gamma and Weibull distribution having two parameters. There is low variation in observed and expected frequency of Normal distribution in bar diagram. Similarly, calculated value of chi-square test (goodness of fit) is observed which is lower in Normal distribution. Furthermore, plot of PDFof Normal distribution covers larger area of histogram than all of other distribution. Hence Normal distribution is the best fit to predict the hemoglobin level in future.

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 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 Critérios para Escolha de Distribuições de Probabilidades em Estudos de Eventos Extremos de Precipitação

2018 ◽  
Vol 33 (4) ◽  
pp. 601-613 ◽  
Author(s):  
Marcel Carvalho Abreu ◽  
Roberto Avelino Cecílio ◽  
Fernando Falco Pruski ◽  
Gérson Rodrigues dos Santos ◽  
Laura Thebit de Almeida ◽  
...  
Keyword(s):  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Log Normal

Resumo Este estudo objetivou estabelecer um critério sobre qual teste de aderência deve ser preferido na escolha de funções de distribuição de probabilidades (fdp). Para tal, foram ajustadas as fdp: Gumbel (GUM), Generalizada de valores extremos (GEV) e Log-normal a 2 parâmetros (LN2), através dos métodos dos momentos, momentos-L e máxima verossimilhança, em séries de precipitação diária máxima anual de 11 estações localizadas na bacia hidrográfica do rio Sapucaí. A aderência dessas fdp aos dados foi feita pelos testes de Kolmogorov-Smirnov (KS), Qui-quadrado (χ2), Filliben (Fi) e Anderson-Darling (AD). Verificaram-se quais testes de aderência são mais rigorosos na seleção de distribuições de probabilidade e, ainda, os testes de aderência que convergem os resultados para a escolha da fdp com melhor desempenho na análise de incerteza e/ou nas estatísticas de ajuste. Os testes de aderência mais rigorosos no aceite da aderência da fdp aos dados são os testes de Fi e AD. O teste de Fi é o que mais converge para a escolha da fdp com melhor desempenho na análise de incerteza e nas estatísticas de ajuste, seguido pelo teste de χ2, portanto devem ser preferidos. As fdp GUM e GEV se destacaram em representar os dados de precipitação máxima anual.

scholarly journals A Comparison of Moment-Independent and Variance-Based Global Sensitivity Analysis Approaches for Wheat Yield Estimation with the Aquacrop-OS Model

Agronomy ◽  
2020 ◽  
Vol 10 (4) ◽  
pp. 607
Author(s):  
Deepak Upreti ◽  
Stefano Pignatti ◽  
Simone Pascucci ◽  
Massimo Tolomio ◽  
Zhenhai Li ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Distribution Function ◽  
Global Sensitivity Analysis ◽  
Global Sensitivity ◽  
Kolmogorov Smirnov ◽  
Anderson Darling ◽  
Parameter Approach ◽  
Influential Parameters ◽  
Smirnov Statistic ◽  
Stress Parameters

The present work reports the global sensitivity analysis of the Aquacrop Open Source (AOS) model, which is the open-source version of the original Aquacrop model developed by the Food and Agriculture Organization (FAO). Analysis for identifying the most influential parameters was based on different strategies of global SA, density-based and variance-based, for the wheat crop in two different geographical locations and climates. The main objectives were to distinguish the model’s influential and non-influential parameters and to examine the yield output sensitivity. We compared two different methods of global sensitivity analysis: the most commonly used variance-based method, EFAST, and the moment independent density-based PAWN method developed in recent years. We have also identified non-influential parameters using Morris screening method, so to provide an idea of the use of non-influential parameters with a dummy parameter approach. For both the study areas (located in Italy and in China) and climates, a similar set of influential parameters was found, although with varying sensitivity. When compared with different probability distribution functions, the probability distribution function of yield was found to be best approximated by a Generalized Extreme Values distribution with Kolmogorov–Smirnov statistic of 0.030 and lowest Anderson–Darling statistic of 0.164, as compared to normal distribution function with Kolmogorov–Smirnov statistic of 0.122 and Anderson–Darling statistic of 4.099. This indicates that yield output is not normally distributed but has a rather skewed distribution function. In this case, a variance-based approach was not the best choice, and the density-based method performed better. The dummy parameter approach avoids to use a threshold as it is a subjective question; it advances the approach to setting up a threshold and gives an optimal way to set up a threshold and use it to distinguish between influential and non-influential parameters. The highly sensitive parameters to crop yield were specifically canopy and phenological development parameters, parameters that govern biomass/yield production and temperature stress parameters rather than root development and water stress parameters.

scholarly journals Tests of Fit for the Logarithmic Distribution

2008 ◽  
Vol 2008 ◽  
pp. 1-8 ◽  
Author(s):  
D. J. Best ◽  
J. C. W. Rayner ◽  
O. Thas
Keyword(s):  
Distribution Function ◽  
Generating Function ◽  
Probability Generating Function ◽  
Smooth Tests ◽  
The Third ◽  
Chi Squared ◽  
Logarithmic Distribution ◽  
Anderson Darling ◽  
Tests Of Fit ◽  
Integrated Distribution Function

Smooth tests for the logarithmic distribution are compared with three tests: the first is a test due to Epps and is based on a probability generating function, the second is the Anderson-Darling test, and the third is due to Klar and is based on the empirical integrated distribution function. These tests all have substantially better power than the traditional Pearson-Fisher X2 test of fit for the logarithmic. These traditional chi-squared tests are the only logarithmic tests of fit commonly applied by ecologists and other scientists.

scholarly journals The Probability Distribution of Maximum Temperature to Assess the Suitable Statistical Models: Take the North-East and Southern Regions of Pakistan

2021 ◽  
Author(s):  
Tasir khan ◽  
Yejuan Wang
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Weibull Distribution ◽  
Statistical Models ◽  
Maximum Temperature ◽  
Kumaraswamy Distribution ◽  
North East ◽  
The North ◽  
Temperature Observation ◽  
Best Fit

Abstract Precise maximum temperature probability distribution information is indeed of accurately significance for numerous temperature uses. The purpose of this research to assess the appropriateness of these functions likelihood for evaluating the temperature models at different sites in southern part of Pakistan. The Kumaraswamy distribution function is used initially to approximation the models of maximum temperature. Compare the presentation of the Kumaraswamy distribution with twelve commonly used the probability functions. The consequences obtained show that the more effective functions are not similar across all sites. The maximum temperature features, quality and quantity of the noted temperature observation can be regarded as a factors that affect the presentation of the function. Similarly, the skewness of the noted maximum temperature observations may affect the precision of Kumaraswamy distribution. For the Hyderabad, Lahore and Sialkot sites, the Kumaraswamy distribution obtainable the topmost presentation, however for the Karachi, Multan stations, the generalized extreme value (GEV) distributions provided the best fit, respectively. According to the calculations, the Kumaraswamy distribution usually be regarded as a valid distribution because it runs 3 best fit sites and ranks 2 to 3 among the remaining sites. Though, the tight presentation of the Kumaraswamy and GEV and the flexibility of the Weibull distribution which has been usually verified, more evaluations of the presentation of the Kumaraswamy distribution are needed.

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