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).

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.

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 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 Prediction of Hydraulic Automatic Transmission Reliability Using Failure Data Based on Exponential Decay Oscillation Distribution Model

2021 ◽  
Vol 2021 ◽  
pp. 1-22
Author(s):  
Yongming Liu ◽  
Guowen Ye ◽  
Zhuanzhe Zhao
Keyword(s):  
Probability Distribution ◽  
Frequency Domain ◽  
Exponential Decay ◽  
Failure Time ◽  
Automatic Transmission ◽  
Oscillation Amplitude ◽  
Distribution Model ◽  
Distribution Characteristics ◽  
Distribution Models ◽  
Mechanical Products

Aiming at the problem that the traditional reliability models of mechanical products are used to predict the reliability of hydraulic automatic transmission and the expected result is relatively large, firstly, the empirical distribution model line is used to statistically analyze the failure distribution law of the hydraulic automatic transmission; then, the Fourier transform is used to perform frequency domain analysis on experience distribution; on this basis, comprehensively consider the characteristics of experience distribution and frequency domain characteristics of experience distribution, constructs the reliability model of exponential decay oscillation distribution and the corresponding reliability, failure efficiency and average life calculation model; meanwhile, studies the influence of attenuation coefficient, oscillation amplitude, oscillation angle frequency, and other parameters on the probability distribution characteristics. On this basis, the established probability distribution models are adopted to fit the failure time data of hydraulic automatic gearbox carried by a forklift, and the fitting results are compared with exponential distribution models, three-parameter Weibull models, and “bathtub curve” models. The comparing results show that the established exponential decayed oscillation distribution model can better describe the probability distribution characteristics of the fault-free working time of automatic transmission, and the use of this model can obtain a smaller root mean square error. Simultaneously, the research conclusions of this paper can provide meaningful guidance and reference for the analysis of the life distribution model of mechanical products with exponentially attenuated oscillation probability density change law.

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 Performance of the probability distribution models applied to heavy rainfall daily events

2014 ◽  
Vol 38 (4) ◽  
pp. 335-342 ◽  
Author(s):  
Rosângela Francisca de Paula Vitor Marques ◽  
Carlos Rogério de Mello ◽  
Antônio Marciano da Silva ◽  
Camila Silva Franco ◽  
Alisson Souza de Oliveira
Keyword(s):  
Probability Distribution ◽  
Heavy Rainfall ◽  
Daily Rainfall ◽  
Distribution Model ◽  
Distribution Models ◽  
Rain Gauges ◽  
Daily Events ◽  
Chi Squared ◽  
L Moments ◽  
Erosive Rainfall

Probabilistic studies of hydrological variables, such as heavy rainfall daily events, constitute an important tool to support the planning and management of water resources, especially for the design of hydraulic structures and erosive rainfall potential. In this context, we aimed to analyze the performance of three probability distribution models (GEV, Gumbel and Gamma two parameter), whose parameters were adjusted by the Moments Method (MM), Maximum Likelihood (ML) and L - Moments (LM). These models were adjusted to the frequencies from long-term of maximum daily rainfall of 8 rain gauges located in Minas Gerais state. To indicate and discuss the performance of the probability distribution models, it was applied, firstly, the non-parametric Filliben test, and in addition, when differences were unidentified, Anderson-Darlling and Chi-Squared tests were also applied. The Gumbel probability distribution model showed a better adjustment for 87.5% of the cases. Among the assessed probability distribution models, GEV fitted by LM method has been adequate for all studied rain gauges and can be recommended. Considering the number of adequate cases, MM and LM methods had better performance than ML method, presenting, respectively, 83% and 79.2% of adequate cases.

scholarly journals Quantization for a Mixture of Uniform Distributions Associated with Probability Vectors

2020 ◽  
Vol 15 (1) ◽  
pp. 105-142
Author(s):  
Mrinal Kanti Roychowdhury ◽  
Wasiela Salinas
Keyword(s):  
Probability Distribution ◽  
Probability Distributions ◽  
Discrete Distribution ◽  
Uniform Distributions ◽  
Basic Goal ◽  
Optimal Quantization ◽  
Finite Set ◽  
Mixed Distributions

AbstractThe basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus approximation of a continuous probability distribution by a discrete distribution. Mixtures of probability distributions, also known as mixed distributions, are an exciting new area for optimal quantization. In this paper, we investigate the optimal quantization for three different mixed distributions generated by uniform distributions associated with probability vectors.

Combining Probability Values from Independent Permutation Tests: A Discrete Analog of Fisher's Classical Method

2004 ◽  
Vol 95 (2) ◽  
pp. 449-458 ◽  
Author(s):  
Paul W. Mielke ◽  
Janis E. Johnston ◽  
Kenneth J. Berry
Keyword(s):  
Probability Distribution ◽  
Classical Method ◽  
Probability Distributions ◽  
Permutation Tests ◽  
Discrete Analog ◽  
Data Sets ◽  
Exact Probability ◽  
Discrete Probability ◽  
Discrete Probability Distributions ◽  
Independent Probability

Permutation tests are based on all possible arrangements of observed data sets. Consequently, such tests yield exact probability values obtained from discrete probability distributions. An exact nondirectional method to combine independent probability values that obey discrete probability distributions is introduced. The exact method is the discrete analog to Fisher's classical method for combining probability values from independent continuous probability distributions. If the combination of probability values includes even one probability value that obeys a sparse discrete probability distribution, then Fisher's classical method may be grossly inadequate.

scholarly journals Uncertainty Analysis for Data-Driven Chance-Constrained Optimization

2020 ◽  
Vol 12 (6) ◽  
pp. 2450
Author(s):  
Bartolomeus Häussling Löwgren ◽  
Joris Weigert ◽  
Erik Esche ◽  
Jens-Uwe Repke
Keyword(s):  
Probability Distribution ◽  
Uncertainty Analysis ◽  
Constrained Optimization ◽  
Process Model ◽  
Data Driven ◽  
Distribution Model ◽  
Chance Constraint ◽  
Distribution Models ◽  
Complex Models ◽  
Increase In Accuracy

In this contribution our developed framework for data-driven chance-constrained optimization is extended with an uncertainty analysis module. The module quantifies uncertainty in output variables of rigorous simulations. It chooses the most accurate parametric continuous probability distribution model, minimizing deviation between model and data. A constraint is added to favour less complex models with a minimal required quality regarding the fit. The bases of the module are over 100 probability distribution models provided in the Scipy package in Python, a rigorous case-study is conducted selecting the four most relevant models for the application at hand. The applicability and precision of the uncertainty analyser module is investigated for an impact factor calculation in life cycle impact assessment to quantify the uncertainty in the results. Furthermore, the extended framework is verified with data from a first principle process model of a chloralkali plant, demonstrating the increased precision of the uncertainty description of the output variables, resulting in 25% increase in accuracy in the chance-constraint calculation.

scholarly journals Clutter Distribution Analysis of A Tropical Foliage Clutter for Different Profiles Based on FSR Micro-Sensor Network

2018 ◽  
Vol 7 (3.7) ◽  
pp. 72
Author(s):  
Nur Alia Zulkifli ◽  
N E. Abd Rashid ◽  
Z I. Khan ◽  
N N. Ismail ◽  
R S. A. Raja Abdullah ◽  
...  
Keyword(s):  
High Frequency ◽  
Free Space ◽  
Distribution Model ◽  
Distribution Analysis ◽  
Distribution Models ◽  
Very High Frequency ◽  
Forward Scatter ◽  
Micro Sensor ◽  
Log Normal ◽  
Very High

Comparison of four different clutter profiles (border, seaside, free space and forest) using Forward Scatter Radar (FSR), which operates in Ultra-High and Very High Frequency (UHF and VHF) bands, is analyzed in this paper. Clutter levels ranging from low, medium, strong and very strong on each profile were studied. Based on the standard deviation of each clutter profile, border suits the best profile as the strongest clutter profile amidst seaside and free space, while the forest is determined as the lowest clutter profile. Subsequently, the characteristics of the clutter are investigated and compared based on the five distribution models (Log-Normal, Log-Logistic, Gamma, Weibull and Nakagami).  The parameters of the five distributions are evaluated using Root Mean Square Error (RMSE) in order to prove that the distribution model fits best to the clutter data. It can be concluded that Gamma distribution is the best distribution model for all cases of frequency bands and profiles.  

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