Chapter 1: Introduction to Statistical Hydrology
1.1 Hydrologic Processes and Phenomena
1.2 Hydrological Variables
1.3 Hydrological Series
1.4 Population and Samples
1.5 Hydrological Data
Chapter 2: Preliminary Analysis of Hydrological Data
2.1 Graphical Depiction of Hydrological Data
2.2 Numeric Summaries and Descriptive Statistics
2.3 Exploratory Methods
2.4 Associations between Variables
Chapter 3: Elementary Theory of Probability
3.1 Random Events
3.2 Notion and Measure of Probability 3.3 Conditional Probability and Statistical Independence
3.4 Total Probability and Bayes Theorems
3.5 Random Variables
3.6 Population Measures of Random Variables
3.7 Joint Probability Distribution Functions
3.7 Probability Distributions of Functions of Random Variables
Chapter 4: Discrete Random Variables: Distributions and Applications
4.1 The Bernoulli Processes and Related Probability Distributions
4.2 The Poisson Process and Related Probability Distributions
4.3 The Hypergeometric and Multinomial Probability Distributions
4.4 Summary of Main Characteristics of Discrete Probability Distributions Chapter 5: Continuous Random Variables: Distributions and Applications
5.1 Uniform Distribution
5.2 Normal Distribution
5.3 Log-Normal Distribution
5.4 Exponential Distribution
5.5 Gamma Distribution
5.6 Beta Distribution
5.7 Extremal Distributions
5.8 Pearson Distributions
5.9 Distributions of Sample Statistics
5.10 The Bivariate Normal Distribution
5.11 Summary of Main Characteristics of Continuous Probability Distributions
Chapter 6: Parameter Estimation
6.1 Overview of Parameter Point Estimation
6.2 Method of Moments
6.3 Method of Maximum Likelihood
6.4 L-Moment Method
6.5 Confidence Interval for Quantiles
6.6 Summary of Point Estimation for Common Probability Distributions
Chapter 7: Hypothesis Testing
7.1 Elements of Hypothesis Testing
7.2 Some Parametric Tests for Normal Populations
7.3 Some Non-Parametric Tests for Hydrological Random Variables
7.4 Some Goodness of Fit of Distributions (Models) 7.5 Detection and Identification of Outliers in Hydrological Samples
Chapter 8: At-Site Frequency Analysis of Hydrological Variables
8.1 At-Site Frequency Analysis with Probability Charts
8.2 Analytic At-Site Frequency Analysis
8.3 At-Site Frequency Analysis with Frequency Factors
8.4 Calculation of Confidence Intervals for Quantiles
8.5 At-Site Frequency Analysis of Partial Duration Series Chapter 9: Correlation and Regression
9.1 Pearson Correlation Coefficient
9.2 Simple Linear Regression
9.3 Coefficient of Determination 9.4 Base Hypotheses for Analysing Simple Linear Regression
9.5 Testing Hypotheses on Coefficients of Simple Linear Regression
9.6 Simple Linear Regression Evaluation
9.7 Non-Linear Regression
9.8 Multiple Linear Regression
Chapter 10: Regional Frequency Analysis of Hydrological Variables
10.1 The Rationale of Regional Frequency Analysis
10.2 Identifying Homogeneous Regions
10.2.1 Geographical Convenience
10.2.2 Subjective Grouping
10.2.3 Objective Grouping
10.2.4 Cluster Analysis 10.2.5 Other Methods
10.3 Methods for Regional Analysis
10.3.1 Method for Regionalizing Quantiles Associated with a Specified Risk
10.3.2 Method of Regionalizing the Parameters of Probability Distributions
10.3.3 Index-Flood Method&n
About the Author: Prof. Dr. Mauro da Cunha Naghettini: Civil Engineer, Federal University of Minas Gerais, Belo Horizonte, Brazil, 1977. MSc in Applied Hydrology, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland, 1979. PhD in Civil and Environmental Engineering, University of Colorado at Boulder, Boulder, USA, 1994. From 1979 to 1989: Engineering Hydrologist at CEMIG, the Minas Gerais State power company. From 1989 to 2014: Professor of Civil and Environmental Engineering at the Brazilian Federal University of Minas Gerais with teaching, research and management responsibilities. Retired in 2014.
