Cover; Half-title; Title page; Copyright information; Dedication; Contents; Preface; Acknowledgments; Part One Theory; 1 Introduction; 1.1 Need for Copulas; 1.2 Introduction of Copulas and Their Application; 1.2.1 Development and Applications of Copulas in Statistics and Finance; 1.2.2 Construction and Parameter Estimation of Copulas; 1.2.3 Application of Copulas in Water Resources Engineering; Copula Applications in Flood Frequency Analysis; Copula Application to Precipitation and Storm Characteristics Analysis; Copula Application to Drought Characteristics Analysis
Copula Application in Other Fields Related to Water Resources Engineering1.3 Theme of the Book; References; Additional Reading; 2 Preliminaries; 2.1 Univariate Probability Distributions; 2.1.1 Normal Distribution; 2.1.2 Log-Normal Distribution; 2.1.3 Student t Distribution; 2.1.4 Exponential and Gamma Distributions; 2.1.5 Generalized Extreme Value (GEV) and Extreme Value (EV) Distributions; EV I Distribution (b = 0); EV II Distribution (b 0); 2.1.6 Weibull Distribution; Pearson and Log-Pearson Type III Distributions; Pearson Type III Distribution
Log-Pearson Type III Distribution2.1.7 Burr XII Distribution; 2.1.8 Log-Logistic Distribution; 2.1.9 Pareto Distribution; 2.2 Bivariate Distributions; 2.2.1 Bivariate Gamma Distribution; Izawa Bigamma Model; Moran Model; Smith-Adelfang-Tubbs (SAT) Model; Farlie-Gumbel-Morgenstern (FGM) Model; Gumbel Mixed (GM) Model; Gumbel Logistic (GL) Model; Bivariate Exponential Model; Nagao-Kadoya Bivariate Exponential (BVE) Model; 2.2.2 Bivariate Normal Distribution; 2.2.3 Bivariate Log-Normal Distribution; 2.3 Estimation of Parameters of Probability Distributions; 2.3.1 Method of Moments
2.3.2 Method of Maximum Likelihood Estimation2.3.3 Probability Weighted Moments Method; 2.3.4 Method of L-Moments; 2.4 Goodness-of-Fit Measures for Probability Distributions; 2.4.1 Goodness-of-Fit Measures for Univariate Probability Distributions; Kolmogorov-Smirnov (KS) Statistic DN; Cramér-von Mises (CM) Statistic W2N; Anderson-Darling (AD) Statistic A2N; Modified Weighted Watson Statistic U2N; Liao and Shimokawa Statistic LN; 2.4.2 Goodness-of-Fit Measures for Bivariate Probability Distributions; Chi-Square Goodness-of-Fit Test; Bivariate (Multivariate) KS Goodness-of-Fit Test
Chi-Square TestBivariate KS goodness-of-fit test; 2.5 Quantile Estimation; 2.6 Confidence Intervals; 2.7 Bias and Root Mean Square Error (RMSE) of Parameter Estimates; 2.8 Risk Analysis; 2.8.1 Univariate Risk Analysis through Return Period; 2.8.2 Bivariate (Multivariate) Risk Analysis through Return Period; ''OR'' Case (X ≥ x ⋃ Y ≥ y); ''AND'' Case: (X ≥ x ⋂ Y ≥ y); ''CONDITIONAL'' Case; References; 3 Copulas and Their Properties; 3.1 Definition of Copulas; 3.1.1 Bivariate Copula; 3.1.2 Trivariate Copula; 3.2 Construction of Copulas; 3.2.1 Inversion Method; 3.2.2 Geometric Method
Summary
Illustration of copula theory with detailed real-world case study examples in the fields of hydrology and water resources engineering
Bibliography
Includes bibliographical references and index
Notes
Online resource; title from digital title page (viewed on March 01, 2019)
