scholarly journals Comparative Evaluation of Probability Distribution Models of Flood flow in Lower Niger Basin

2021 ◽  
Vol 6 (2) ◽  
pp. 107-117
Author(s):  
Itolima Ologhadien
Keyword(s):  
Water Resources ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Model ◽  
Distribution Models ◽  
Optimum Distribution ◽  
Water Resources Systems ◽  
Type Iii ◽  
Pearson Type

The choice of optimum probability distribution model that would accurately simulate flood discharges at a particular location or region has remained a challenging problem to water resources engineers. In practice, several probability distributions are evaluated, and the optimum distribution is then used to establish the quantile - probability relationship for planning, design and management of water resources systems, risk assessment in flood plains and flood insurance. This paper presents the evaluation of five probability distributions models: Gumbel (EV1), 2-parameter lognormal (LN2), log pearson type III (LP3), Pearson type III(PR3), and Generalised Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of five hydrological stations in the lower Niger River Basin in Nigeria. The choice of optimum probability distribution model was made on five statistical goodness – of – fit measures; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR), and probability plot correlation coefficient (PPCC). The results show that GEV is the optimum distribution in 3 stations, and LP3 in 2 stations. On the overall GEV is the best – fit distribution, seconded by PR3 and thirdly, LP3. Furthermore, GEV simulated discharges were in closest agreement with the observed flood discharges. It is recommended that GEV, PR3 and LP3 should be considered in the final selection of optimum probability distribution model in Nigeria.

scholarly journals Flood Flow Probability Distribution Model Selection on Niger/Benue River Basins in Nigeria

2021 ◽  
pp. 76-94
Author(s):  
Itolima Ologhadien
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
River Basins ◽  
Flood Frequency ◽  
Flood Frequency Analysis ◽  
Distribution Model ◽  
Distribution Models ◽  
Type Iii ◽  
Pearson Type ◽  
Best Fit

Flood frequency analysis is a crucial component of flood risk management which seeks to establish a quantile relationship between peak discharges and their exceedance (or non-exceedance) probabilities, for planning, design and management of infrastructure in river basins. This paper evaluates the performance of five probability distribution models using the method of moments for parameter estimation, with five GoF-tests and Q-Q plots for selection of best –fit- distribution. The probability distributions models employed are; Gumbel (EV1), 2-parameter lognormal (LN2), log Pearson type III (LP3), Pearson type III(PR3), and Generalised Extreme Value( GEV). The five statistical goodness – of – fit tests, namely; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR) were used to identify the most suitable distribution models. The study was conducted using annual maximum series of nine gauge stations in both Benue and Niger River Basins in Nigeria. The study reveals that GEV was the best – fit distribution in six gauging stations, LP3 was best – fit distribution in two gauging stations, and PR3 is best- fit distribution in one gauging station. This study has provided a significant contribution to knowledge in the choice of distribution models for predicting extreme hydrological events for design of water infrastructure in Nigeria. It is recommended that GEV, PR3 and LP3 should be considered in the development of regional flood frequency using the existing hydrological map of Nigeria.

scholarly journals A best-fit probability distribution for the estimation of rainfall in northern regions of Pakistan

2016 ◽  
Vol 11 (1) ◽  
pp. 432-440 ◽  
Author(s):  
M. T. Amin ◽  
M. Rizwan ◽  
A. A. Alazba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Future Research ◽  
Maximum Rainfall ◽  
Type Iii ◽  
Goodness Of Fit Tests ◽  
Pearson Type ◽  
Northern Regions ◽  
Best Fit

AbstractThis study was designed to find the best-fit probability distribution of annual maximum rainfall based on a twenty-four-hour sample in the northern regions of Pakistan using four probability distributions: normal, log-normal, log-Pearson type-III and Gumbel max. Based on the scores of goodness of fit tests, the normal distribution was found to be the best-fit probability distribution at the Mardan rainfall gauging station. The log-Pearson type-III distribution was found to be the best-fit probability distribution at the rest of the rainfall gauging stations. The maximum values of expected rainfall were calculated using the best-fit probability distributions and can be used by design engineers in future research.

scholarly journals Best Fitted Distribution For Meteorological Data In Kuala Krai

2021 ◽  
Vol 3 (1) ◽  
pp. 16-25
Author(s):  
Siti Mariam Norrulashikin ◽  
Fadhilah Yusof ◽  
Siti Rohani Mohd Nor ◽  
Nur Arina Bazilah Kamisan
Keyword(s):  
Climate Change ◽  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Meteorological Data ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Data Series ◽  
Distribution Models ◽  
Goodness Of Fit Tests

Modeling meteorological variables is a vital aspect of climate change studies. Awareness of the frequency and magnitude of climate change is a critical concern for mitigating the risks associated with climate change. Probability distribution models are valuable tools for a frequency study of climate variables since it measures how the probability distribution able to fit well in the data series. Monthly meteorological data including average temperature, wind speed, and rainfall were analyzed in order to determine the most suited probability distribution model for Kuala Krai district. The probability distributions that were used in the analysis were Beta, Burr, Gamma, Lognormal, and Weibull distributions. To estimate the parameters for each distribution, the maximum likelihood estimate (MLE) was employed. Goodness-of-fit tests such as the Kolmogorov-Smirnov, and Anderson-Darling tests were conducted to assess the best suited model, and the test's reliability. Results from statistical studies indicate that Burr distributions better characterize the meteorological data of our research. The graph of probability density function, cumulative distribution function as well as Q-Q plot are presented.

scholarly journals Selection Selection of Probabilistic Model of Extreme Floods in Benue River Basin, Nigeria

2021 ◽  
Vol 6 (1) ◽  
pp. 7-18
Author(s):  
Itolima Ologhadien
Keyword(s):  
Probability Distribution ◽  
River Basin ◽  
Frequency Analysis ◽  
Probabilistic Model ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Model ◽  
Extreme Floods ◽  
Pearson Type ◽  
Selection Of

The selection of optimum probabilistic model of extreme floods as a crucial step for flood frequency analysis has remained a formidable challenge for the scientific and engineering communities to address. Presently, there is no scientific consensus about the choice of probability distribution model that would accurately simulate flood discharges at a particular location or region. In practice, several probability distributions are evaluated, and the optimum distribution is then used to establish the design quantile - probability relationship. This paper presents the evaluation of five probability distributions models; Gumbel (EV1), 2-parameter lognormal (LN2), log Pearson type III (LP3), Pearson type III(PR3), and Generalized Extreme Value (GEV) using the method of moments (MoM) for parameter estimation and annual maximum series of four hydrological stations in Benue River Basin in Nigeria. Additionally, Q-Q plots were used to compliment the selection process. The choice of optimum probability distribution model was based on five statistical goodness – of – fit measures; modified index of agreement (Dmod), relative root mean square error (RRMSE), Nash – Sutcliffe efficiency (NSE), Percent bias (PBIAS), ratio of RMSE and standard deviation of the measurement (RSR). Goodness – of – fit assessment reveals that GEV is the best – fit distribution, seconded by PR3 and thirdly, LP3. In comparison with WMO (1989) survey of countries on distribution types currently in use for frequency analysis of extremes of floods shows that GEV is standard in one country, while PR3 is a standard in 7 countries, and LP3 is standard in 7 countries. It is recommended that GEV, PR3 and LP3 should be considered in the final selection of optimum probability distribution model in Nigeria.

Risk Planning with Discrete Distribution Analysis Applied to Petroleum Spills

2013 ◽  
Vol 2 (4) ◽  
pp. 61-78 ◽  
Author(s):  
Roy L. Nersesian ◽  
Kenneth David Strang
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Low Cost ◽  
Discrete Distribution ◽  
Distribution Model ◽  
Distribution Analysis ◽  
Distribution Models ◽  
Discrete Probability ◽  
Nonparametric Statistical ◽  
Spreadsheet Software

This study discussed the theoretical literature related to developing and probability distributions for estimating uncertainty. A theoretically selected ten-year empirical sample was collected and evaluated for the Albany NY area (N=942). A discrete probability distribution model was developed and applied for part of the sample, to illustrate the likelihood of petroleum spills by industry and day of week. The benefit of this paper for the community of practice was to demonstrate how to select, develop, test and apply a probability distribution to analyze the patterns in disaster events, using inferential parametric and nonparametric statistical techniques. The method, not the model, was intended to be generalized to other researchers and populations. An interesting side benefit from this study was that it revealed significant findings about where and when most of the human-attributed petroleum leaks had occurred in the Albany NY area over the last ten years (ending in 2013). The researchers demonstrated how to develop and apply distribution models in low cost spreadsheet software (Excel).

Best-fit probability distribution model for predicting annual maximum rainfall of Pusa (Bihar)

2018 ◽  
Vol 3 (01) ◽  
pp. 100-104
Author(s):  
J. Kumar ◽  
R. Suresh ◽  
Jyoti .
Keyword(s):  
Probability Distribution ◽  
Gumbel Distribution ◽  
Annual Rainfall ◽  
Annual Maximum ◽  
Distribution Models ◽  
Maximum Rainfall ◽  
Type Iii ◽  
Pearson Type ◽  
Annual Maximum Rainfall ◽  
Pearson Type Iii Distribution

In present study an attempt has been made to evaluate the suitable probability distribution models for predicting 1, 2, 3, 4, 5, 6 and 7-days annual maximum rainfall amounts based on 39 years (1964 to 2002) daily rainfall data. Three probability distribution models namely: Log Normal distribution, Log Pearson Type-III distribution and Gumbel distribution models were considered to evaluate their goodness of fit. The Weibull’s method was used for computation of observed rainfall values at1, 5, 20, 30, 50, 95 and 99 percent probability levels. The Log Pearson type –III distribution was found suitable for 1 and 2 days maximum annual rainfall, while Gumbel distribution was found to be the best for predicting 3, 4, 5, 6 and 7- days annual maximum rainfall amounts. The relationships between annual maximum rainfall and return periods were also developed. The non – linear relationships (i.e. logarithmic) were found to be most suitable for all the cases.

scholarly journals Best fitting probability distributions for annual maximum discharge data of the river Kopili, Assam

2009 ◽  
Vol 1 (1) ◽  
pp. 50-52
Author(s):  
Abhijit Bhuyan ◽  
Munindra Borah
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Annual Maximum ◽  
Discharge Data ◽  
Generalized Pareto ◽  
Maximum Discharge ◽  
Pearson Type ◽  
Best Fitting ◽  
Log Normal

In this study our main objective is to determine the best fitting probability distribution for annual maximum flood discharge data of river Kopili, Assam. Various probability distributions i.e. Gumbel (G), generalized extreme value (GEV), normal (N), log-normal (LN3), generalized logistic (GLO), generalized pareto (GPA) and Pearson type-III (PE3) have been used for our study. The L-moments methods have been used for estimating the parameters of all the distributions. The root mean square error (RMSE), model efficiency and D-index (fit in the top six values) together with L-moment ratio diagram is used for goodness of fit measure. It has been observed that Generalized Pareto is the best fitting probability distribution for annual maximum discharge data of river Kopili.

The Hydrometeorology of the Kariba Catchment Area Based on the Probability Distributions

2015 ◽  
Vol 19 (4) ◽  
pp. 1-18 ◽  
Author(s):  
S. Muchuru ◽  
C. M. Botai ◽  
J. O. Botai ◽  
A. M. Adeola
Keyword(s):  
Probability Distribution ◽  
Catchment Area ◽  
Probability Distributions ◽  
Water Levels ◽  
Distribution Model ◽  
Data Series ◽  
Distribution Models ◽  
Best Fit ◽  
Zambezi River Basin ◽  
Zambezi River

Abstract In this paper, monthly, maximum seasonal, and maximum annual hydrometeorological (i.e., evaporation, lake water levels, and rainfall) data series from the Kariba catchment area of the Zambezi River basin, Zimbabwe, have been analyzed in order to determine appropriate probability distribution models of the underlying climatology from which the data were generated. In total, 16 probability distributions were considered and the Kolmogorov–Sminorv (KS), Anderson–Darling (AD), and chi-square (χ2) goodness-of-fit (GoF) tests were used to evaluate the best-fit probability distribution model for each hydrometeorological data series. A ranking metric that uses the test statistic from the three GoF tests was formulated and used to select the most appropriate probability distribution model capable of reproducing the statistics of the hydrometeorological data series. Results showed that, for each hydrometeorological data series, the best-fit probability distribution models were different for the different time scales, corroborating those reported in the literature. The evaporation data series was best fit by the Pearson system, the Lake Kariba water levels series was best fit by the Weibull family of probability distributions, and the rainfall series was best fit by the Weibull and the generalized Pareto probability distributions. This contribution has potential applications in such areas as simulation of precipitation concentration and distribution and water resources management, particularly in the Kariba catchment area and the larger Zambezi River basin, which is characterized by (i) nonuniform distribution of a network of hydrometeorological stations, (ii) significant data gaps in the existing observations, and (iii) apparent inherent impacts caused by climatic extreme events and their corresponding variability.

scholarly journals Modelling Rainfall Intensity by Optimization Technique in Abeokuta, South-West, Nigeria

2019 ◽  
pp. 1-10
Author(s):  
A. O. David ◽  
Ify L. Nwaogazie ◽  
J. C. Agunwamba
Keyword(s):  
Probability Distribution ◽  
Goodness Of Fit ◽  
Rainfall Intensity ◽  
Mean Squared Error ◽  
Optimization Technique ◽  
Distribution Models ◽  
Goodness Of Fit Test ◽  
Maximum Rainfall ◽  
Pearson Type ◽  
Type 3

The design of water resources engineering control structures is best achieved with adequate estimation of rainfall intensity over a particular catchment. To develop the rainfall intensity, duration and frequency (IDF) models, 25 year daily rainfall data were collected from Nigerian Meteorological Agency (NIMET) Abuja for Abeokuta. The annual maximum rainfall amounts with durations of 5, 10, 15, 20, 30, 45, 60, 90, 120, 180, 240, 300 and 420 minutes were extracted and subjected to frequency analysis using the Excel Optimization Solver wizard. Specific and general IDF models were developed for return periods of 2, 5, 10, 25, 50 and 100 years using the Gumbel Extreme Value Type -1 and Log Pearson Type -3 distributions. The Anderson-Darling goodness of fit test was used to ascertain the best fit probability distribution. The R2 values range from 0.973 – 0.993 and the Mean Squared Error, MSE from 84.49 – 134.56 for the Gumbel and 0.964 – 0.997 with MSE of 42.88 – 118.68 for Log Pearson Type -3 distribution, respectively. The probability distribution models are recommended for the prediction of rainfall intensities for Abeokuta metropolis.

Regression equations of probability plot correlation coefficient test statistics using machine learning

2020 ◽  
Author(s):  
Hyunjun Ahn ◽  
Sunghun Kim ◽  
Joohyung Lee ◽  
Jun-Haeng Heo
Keyword(s):  
Machine Learning ◽  
Probability Distribution ◽  
Sample Size ◽  
Correlation Coefficient ◽  
Goodness Of Fit ◽  
Probability Distributions ◽  
Distribution Model ◽  
Regression Equations ◽  
Probability Plot ◽  
Sample Data

<p>In the extremes hydrology field, it is essential to find the probability distribution model that is most appropriate for the sample data to estimate the reasonable probability quantile. Depending on the assumed probability distribution model, the probability quantile could be estimated with quite different values. The probability plot correlation coefficient (PPCC) test is one of the goodness-of-fit tests for finding suitable probability distributions for a given sample. The PPCC test determines whether assumed probability distributions are acceptable for the sample data using correlation coefficients between sample data and theoretical quantiles of assumed probability distributions. The critical values for identification are presented as a two-dimensional table, depending on the sample size and the shape parameters of models, for a three-parameter probability distribution. In this study, the applicability and utility of machine learning in the hydrology field were examined. For the usability of the PPCC test, a regression equation was derived using a machine learning algorithm with two variables: sample size and shape parameter.</p>

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