Fundamentals of Statistical Hydrology

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

3.3 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

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

7.5 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

Chapter 9: Correlation and Regression

9.1 Pearson Correlation Coefficient

9.2 Simple Linear Regression

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

10.2.5 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 

10.4 The Index-Flood Method with L-Moments

10.4.1 Screening the Data with the Discordancy Measure

10.4.2 Identifying Homogeneous Regions with the Heterogeneity Measure

10.4.3 Choosing the Regional Distribution with the Goodness-of-Fit Measure

10.4.4 Estimating the Regional Frequency Distribution Model

10.4.5 Discussion on Regional Frequency Analysis

Chapter 11: Introduction of Bayesian Analysis and Its Applications in Hydrology

11. 1 Basic Concepts

11.2 Prior Distributions

11.3 Bayesian Estimation and Credibility Intervals

11.4 Calculation Methods for Bayesian Estimation

11.5 Example Applications

Chapter 12: Introduction to the Analysis and Modelling of Nonstationary Hydrological Series

12.1 Methods for Detecting Nonstationarities

12.2 Hypotheses Testing for Monotonic Trends and Change Points

12.3 Kernel Estimation of Poisson Point Process Rates

12.4 Introduction to Generalized Linear Models

12.5 Nonstationary Models Based on Extremal Distributions

12.6 Return Period and Hydrological Risk under Nonstationary Conditions