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Note: Cover -- Half-title -- Title page -- Copyright information -- Dedication -- Contents -- Preface -- Acknowledgments -- 1 Introduction -- 1.1 Random Variables in Environmental and Water Engineering -- 1.1.1 Rainfall -- 1.1.2 Temperature -- 1.1.3 Frost, Fog, and Sunshine Hours -- 1.1.4 Wind -- 1.1.5 Snowfall -- 1.1.6 Runoff -- 1.1.7 Flood -- 1.1.8 Drought -- 1.1.9 Hydrogeology -- 1.1.10 Water Quality -- 1.2 Systems of Frequency Distributions -- 1.2.1 Stoppa System -- 1.2.2 Dagum System -- 1.2.3 Johnson System -- 1.2.4 General Classification -- 1.3 Need for Systems of Frequency Distributions -- 1.4 Organization of the Book -- References -- 2 Pearson System of Frequency Distributions -- 2.1 Introduction -- 2.2 Differential Equation of Pearson System -- 2.3 Generalization of Pearson System -- 2.4 Pearson Distributions -- 2.4.1 Nonnegative Discriminant -- 2.4.2 Negative Discriminant -- 2.4.3 Pearson Type 0 Distribution -- 2.4.4 Pearson Type I Distribution -- 2.4.5 Pearson Type II Distribution -- 2.4.6 Pearson Type III Distribution -- 2.4.7 Pearson Type IV Distribution -- 2.4.8 Pearson Type V Distribution -- 2.4.9 Pearson Type VI Distribution -- 2.4.10 Pearson Type VII Distribution -- 2.4.11 Pearson Type VIII Distribution -- 2.4.12 Pearson Type IX Distribution -- 2.4.13 Pearson Type X Distribution -- 2.4.14 Pearson Type XI Distribution -- 2.4.15 Pearson Type XII Distribution -- 2.5 Graphical Representation of Shapes Based on the Relation of α23 versus d and α23 versus α4 -- 2.5.1 Graphical Representation of Pearson Distributions -- 2.5.2 Type I(U): -- 2.5.3 Type III(B): -- 2.5.4 Type IV(B): -- 2.5.5 Type VI: -- 2.6 Application -- Normal Distribution -- Gamma Distribution -- Pearson III Distribution -- Log-Pearson III Distribution -- 2.7 Conclusion -- References -- 3 Burr System of Frequency Distributions -- 3.1 Introduction. , 3.2 Characteristics of Probability Distribution Functions -- 3.3 Burr Hypothesis -- 3.4 Burr System of Frequency Distributions -- 3.4.1 Burr I Distribution -- 3.4.2 Burr II Distribution -- 3.4.3 Burr III Distribution -- 3.4.4 Burr IV Distribution -- 3.4.5 Burr V Distribution -- 3.4.6 Burr VI Distribution -- 3.4.7 Burr VII Distribution -- 3.4.8 Burr VIII Distribution -- 3.4.9 Burr IX Distribution -- 3.4.10 Burr X Distribution -- 3.4.11 Burr XI Distribution -- 3.4.12 Burr XII Distribution -- 3.5 Parameter Estimation by Cumulative Moment Theory -- 3.6 Application -- 3.6.1 Peak Flow -- 3.6.2 Annual Rainfall Amount -- 3.6.3 Monthly Sediment Yield -- 3.6.4 Maximum Daily Precipitation -- 3.7 Conclusion -- References -- 4 D'Addario System of Frequency Distributions -- 4.1 Introduction -- 4.2 D'Addario System -- 4.2.1 Pareto Type I Distribution -- 4.2.2 Pareto Type II Distribution -- 4.2.3 Lognormal (2-Parameter) Distribution -- 4.2.4 Lognormal (3-Parameter) Distribution -- 4.2.5 Davis Distribution -- 4.2.6 Amoroso Distribution -- 4.3 Application -- 4.3.1 Peak Flow -- 4.3.2 Monthly Discharge -- 4.3.3 Deseasonalized TPN -- 4.3.4 Daily Maximum Precipitation -- 4.4 Conclusion -- References -- 5 Dagum System of Frequency Distributions -- 5.1 Introduction -- 5.2 Dagum System of Distributions -- 5.3 Derivation of Frequency Distributions -- 5.3.1 Pareto Type I Distribution -- 5.3.2 Pareto Type II Distribution -- 5.3.3 Pareto Type III Distribution -- 5.3.4 Benini Distribution -- 5.3.5 Weibull Distribution -- 5.3.6 Log-Gompertz Distribution -- 5.3.7 Fisk Distribution -- 5.3.8 Singh-Maddala Distribution -- 5.3.9 Dagum I Distribution -- 5.3.10 Dagum II Distribution -- 5.3.11 Dagum III Distribution -- 5.4 Application -- 5.4.1 Monthly Sediment Yield -- 5.4.2 Peak Flow -- 5.4.3 Maximum Daily Precipitation -- 5.4.4 Drought (Total Flow Deficit) -- 5.5 Conclusion. , References -- 6 Stoppa System of Frequency Distributions -- 6.1 Introduction -- 6.2 Stoppa System of Distributions -- 6.3 Derivation of Frequency Distributions -- 6.3.1 Generalized Power Distribution (Stoppa Type I Distribution) -- 6.3.2 Generalized Pareto Type II Distribution -- 6.3.3 Generalized Exponential Distribution (Type III Distribution) -- 6.3.4 Stoppa Type IV Distribution -- 6.3.5 Stoppa Type V Distribution -- 6.3.6 Four-Parameter Generalized Pareto Distribution -- 6.4 Relation between Dagum and Stoppa Systems -- 6.5 Relations among Burr distributions and Dagum and Stoppa Systems -- 6.6 Application -- 6.6.1 Monthly Suspended Sediment -- 6.6.2 Annual Rainfall Amount -- 6.6.3 Peak Flow -- 6.6.4 Maximum Daily Precipitation -- 6.6.5 Drought (Total Flow Deficit) -- 6.7 Conclusion -- References -- 7 Esteban System of Frequency Distributions -- 7.1 Introduction -- 7.2 Esteban System of Distributions -- 7.2.1 Three-Parameter Gamma Distribution -- 7.2.2 Special Cases of Generalized Gamma Distribution -- 7.2.3 Generalized Beta Distribution of First Kind -- 7.2.4 Special Cases of GB1 Distribution -- 7.2.5 Generalized Beta Distribution of Second Kind -- 7.2.6 Special Cases of GB2 Distribution -- 7.3 Application -- 7.3.1 TPN -- 7.3.2 Peak Flow -- 7.3.3 Drought (Total Flow Deficit) -- 7.3.4 Annual Rainfall -- 7.4 Conclusion -- References -- 8 Singh System of Frequency Distributions -- 8.1 Introduction -- 8.2 Singh System of Distributions -- 8.3 Conclusion -- References -- 9 Systems of Frequency Distributions Using Bessel Functions and Cumulants -- 9.1 Introduction -- 9.2 Bessel Function Distributions -- 9.2.1 Moments of Bessel Function Distributions -- 9.2.2 Bessel Function Line -- 9.2.3 Inverse Gaussian Distribution -- 9.2.4 Other Distributions -- Product of Two Bessel Functions of the First Kind (Im, In). , Product of the Two Bessel Functions of the Second Kind (Km, Kn) -- Product of the Bessel Functions of the First Kind (Im) and the Second Kind (Kn) -- 9.3 Frequency Distributions by Series Approximation -- 9.3.1 Chebyshev (Probabilists')-Hermite Polynomials -- 9.3.2 Cumulants -- 9.3.3 Basic Concept of Approximating Frequency Distribution with Series Approximation -- 9.3.4 Gram-Charlier Type A Series -- 9.3.5 Edgeworth Series with Baseline Gaussian Distribution -- 9.3.6 Gram-Charlier/Edgeworth Series with Non-Gaussian Distribution -- Gamma Distribution as Baseline PDF -- Beta Distribution as Baseline PDF -- 9.4 Applications -- 9.5 Conclusion -- References -- 10 Frequency Distributions by Entropy Maximization -- 10.1 Introduction -- 10.2 Entropy Maximization -- 10.3 Application -- 10.3.1 Peak Flow -- 10.3.2 Monthly Sediment Yield -- 10.4 Conclusion -- References -- 11 Transformations for Frequency Distributions -- 11.1 Introduction -- 11.2 Transformation to Normal Distribution -- 11.3 Transformation of Normal Distribution: The Johnson family -- 11.4 Transformation Based on the First Law of Laplace -- 11.5 Transformation of Logistic Distribution -- 11.6 Transformation of Beta Distribution -- 11.7 Transformation of Gamma Distribution -- 11.8 Transformation of Student-t Distribution -- 11.9 Application -- 11.9.1 Peak Flow and Maximum Daily Precipitation -- 11.9.2 Monthly Sediment and Annual Rainfall -- 11.10 Conclusions -- References -- 12 Genetic Theory of Frequency -- 12.1 Basic Concept of Elementary Errors -- 12.2 General Discussion of Charlier Type A and B Curves -- 12.3 Charlier Type A Curve -- 12.4 Charlier Type B Curve -- 12.5 Extensions by Wicksell -- References -- Appendix Datasets for Applications -- Index.