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Tung, Yeou-Koung and Yen, Ben-Chie. Hydrosystems Engineering Uncertainty Analysis. US: McGraw-Hill Professional, 2005.

Hydrosystems Engineering Uncertainty Analysis

Authors: Yeou-Koung Tung and Ben-Chie Yen

Published:  March 2005

eISBN: 9780071467087 0071467084 | ISBN: 9780071451598
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  • Terms of Use
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  • Contents
  • Preface
  • Acknowledgments
  • Chapter 1. Uncertainties in Hydrosystems Engineering and Management
  • 1.1 Definition of Uncertainty
  • 1.2 Types and Sources of Uncertainty
  • 1.3 Purposes of Uncertainty Analysis
  • 1.4 Measures of Uncertainty
  • 1.5 Implications of Uncertainty
  • 1.6 Overall View of Uncertainty Analysis Methods
  • References
  • Chapter 2. Fundamentals of Probability and Statistics for Uncertainty Analysis
  • 2.1 Basic Concepts of Probability
  • 2.2 Random Variables and Their Distributions
  • 2.2.1 Cumulative Distribution Function and Probability Density Function
  • 2.2.2 Joint, Conditional, and Marginal Distributions
  • 2.3 Statistical Properties of Random Variables
  • 2.3.1 Statistical Moments of Random Variables
  • 2.3.2 Mean, Mode, Median, and Quantiles
  • 2.3.3 Variance, Standard Deviation, and Coefficient of Variation
  • 2.3.4 Skewness Coefficient and Kurtosis
  • 2.3.5 Covariance and Correlation Coefficient
  • 2.4 Some Continuous Univariate Probability Distributions
  • 2.4.1 Normal (Gaussian) Distribution
  • 2.4.2 Lognormal Distribution
  • 2.4.3 Gamma Distribution and Variations
  • 2.4.4 Extreme Value Distributions
  • 2.4.5 Beta Distributions
  • 2.4.6 Distributions Used For Hypothesis Testing
  • 2.5 Commonly Used Multivariate Probability Distributions
  • 2.5.1 Multivariate Normal Distributions
  • 2.5.2 Multivariate Lognormal Distributions
  • Problems
  • References
  • Chapter 3. Regression Analysis
  • 3.1 Introduction
  • 3.2 Identification of Appropriate Models
  • 3.3 Parameters Estimation by the Least Squares Method
  • 3.4 Measures of Goodness-of-Fit
  • 3.5 Uncertainty Features of LS-Based Model Parameters
  • 3.6 Statistical Inferences of Regression Coefficients
  • 3.7 Confidence Interval and Prediction Interval
  • 3.8 Variance Contribution by Independent Variables
  • 3.9 Issues in Regression Analysis
  • 3.9.1 Selection of Explanatory Variables
  • 3.9.2 Model Linearization and Adequacy Check
  • 3.9.3 Multicollinearity and Outliers
  • 3.9.4 Implementation of Regression Analysis
  • Problems
  • References
  • Chapter 4. Analytic Methods for Uncertainty Analysis
  • 4.1 Derived Distribution Method
  • 4.2 Fourier, Laplace, and Exponential Transforms
  • 4.2.1 Fourier Transform and Characteristic Function
  • 4.2.2 Convolution Properties of Characteristic Functions
  • 4.2.3 Laplace and Exponential Transforms and Moment Generating Functions
  • 4.3 Mellin Transform
  • 4.3.1 Statistical Moments and The Mellin Transform
  • 4.3.2 Operational Properties of The Mellin Transform
  • 4.3.3 Mellin Transform of Some Probability Density Functions
  • 4.3.4 Sensitivity of Component Uncertainty on Overall Uncertainty
  • 4.4 Estimations of Probability and Quantile Using Moments
  • 4.4.1 Edgeworth Asymptotic Expansion of PDF and CDF
  • 4.4.2 Fisher-Cornish Asymptotic Expansion of Quantile
  • 4.4.3 Maximum Entropy Distribution
  • 4.5 Concluding Remarks
  • Problems
  • References
  • Chapter 5. Approximation Methods for Uncertainty Analysis
  • 5.1 First-Order Variance Estimation Method
  • 5.1.1 Univariate FOVE Method
  • 5.1.2 Bivariate FOVE Method
  • 5.1.3 Multivariate FOVE Method
  • 5.2 Rosenblueth's Probabilistic Point Estimation Method
  • 5.2.1 Univariate Rosenblueth PE Method
  • 5.2.2 Bivariate Rosenblueth PE Method
  • 5.2.3 Multivariate Rosenblueth PE Method
  • 5.3 Harr's Probabilistic Point Estimation Method
  • 5.3.1 Orthogonal Transformations
  • 5.3.2 Bivariate Harr PE Method
  • 5.3.3 Multivariate Harr PE Method
  • 5.3.4 Modified Harr PE Algorithm
  • 5.4 Li's Probabilistic Point Estimate Method
  • 5.5 Summary and Concluding Remarks
  • Appendix 5A: Cholesky Decomposition
  • Problems
  • References
  • Chapter 6. Monte Carlo Simulation
  • 6.1 Introduction
  • 6.2 Generation of Random Numbers
  • 6.3 Classifications of Random Variates Generation Algorithms
  • 6.3.1 CDF-Inverse Method
  • 6.3.2 Acceptance-Rejection Methods
  • 6.3.3 Variable Transformation Method
  • 6.4 Generation of Univariate Random Numbers for Some Distributions
  • 6.4.1 Normal Distribution
  • 6.4.2 Lognormal Distribution
  • 6.4.3 Exponential Distribution
  • 6.4.4 Gamma Distribution
  • 6.4.5 Other Univariate Distributions and Computer Programs
  • 6.5 Generation of Vector of Multivariate Random Variables
  • 6.5.1 CDF-Inverse Method
  • 6.5.2 Generating Multivariate Normal Random Variates
  • 6.5.3 Generating Multivariate Random Variates with Known Marginal PDFs and Correlations
  • 6.6 Variance-Reduction Techniques
  • 6.6.1 Antithetic-Variates Technique
  • 6.6.2 Correlated-Sampling Techniques
  • 6.6.3 Stratified Sampling Technique
  • 6.6.4 Latin Hypercube Sampling Technique
  • 6.7 Resampling Techniques
  • 6.7.1 Jackknife Method
  • 6.7.2 Bootstrap Technique
  • 6.8 Sensitivity and Uncertainty Analysis by Monte Carlo Simulation
  • Problems
  • References
  • Index
  • About the Authors
  • Notes