1 CHARACTERISTICS OF HYDROLOGIC PHENOMENA
Deterministic and Stochastic Processes of Hydrology
Probability, Determinism and Hydrology
Hydrologic Data
Hydrologic Magnitudes and Cause-Effect Relations
Stochastic Nature of Water Demand
Problems for Discussion and Solutions
2 RANDOM VARIABLES AND THEIR DISTRIBUTIONS ....
Probability and Random Phenomena of Hydrology
Approaches to Probability, and Hydrology
Random Events
Random Variables
Univariate Distributions
Distributions of Bivariates, Multivariates, and Conditional Variables 28
Distributions of Functions of Random Variables
Problems for Discussion and Solutions
3 VARIOUS PROBABILITY TOPICS APPLIED TO HYDROLOGY
Combinatorial Analysis
Geometric Probabilities
Applications of the Theorem of Total Probability and the Bayes's Theorem
Limit Theorems
Markov Chains
Mathematical Expectation, and Variance of Random Variables . .
Law of Large Numbers
Problems for Discussion and Solutions
4 STATISTICS AND HYDROLOGY
Relationship of Statistics to Probability Theory
Statistics as Description Numbers
Mathematical Statistical Models
Concepts of Risk and Uncertainty in Hydrology
Statistics in Hydrology
Problems for Discussion and Solutions
5 EMPIRICAL DISTRIBUTIONS OF HYDROLOGIC VARIABLES
Frequency and Cumulative Frequency Curves of Univariates .
Plotting Empirical Univariate Distributions of Ungrouped Data
Multivariate Frequency Distributions
Methods of Presentation and Analysis of Empirical Distributions
Qualitative Analysis of Frequency Distributions
Problems for Discussion and Solutions
6 PARAMETERS AND ORDER-STATISTICS AS DESCRIPTORS OF DISTRIBUTIONS
Parameters and Order-Statistics
Descriptors of Central Tendency
Descriptors of Dispersion
Descriptors of Asymmetry
Descriptors of Flatness
Application Areas of Descriptors of Univariate Distributions
in Hydrology and Water Resources
6.7 Descriptors of Distributions of Bivariates, Multivariates,
and Conditional Variables
6.8 Problems for Discussion and Solutions
|
|
7 PROBABILITY DISTRIBUTION FUNCTIONS IN HYDROLOGY
Functions for Fitting Empirical Frequency Distributions ....
Properties and Classification of Probability Distriburion Functions
Binomial Distribution
Poisson Distribution
Normal Distribution
Lognormal Distribution
Gamma Distributions
Extreme Value Distributions
Other Univariate Distribution Functions, and Concluding Remarks
Distribution Functions for Bivariates, Multivariates, and Conditional Variables
Problems for Discussion and Solutions
8 ESTIMATION METHODS
Definitions and Properties of Estimates
Graphical Estimation Method
Least-Squares Estimation Method
Method of Moments
Maximum Likelihood Method
Problems for Discussion and Solutions
9 SAMPLING THEORY
Basic Definitions and Approaches
Parameters of Distributions of Basic Statistics
Sampling Distribution Functions
Confidence and Tolerance Intervals and Limits
Content of Information in Various Parameters
Problems for Discussion and Solutions
10 TESTING HYPOTHESES AND GOODNESS OF FIT
Definitions of Hypotheses and Their Testing
Testing Simple and Composite Hypotheses
Testing the Goodness of Fit of Probability Functions to Empirical Distributions
Problems for Discussion and Solutions
11 CORRELATION AND REGRESSION
Definitions of Correlation and Regression
Linear Bivariate Correlation
Spurious Correlation and Interstation Correlation
Linear Bivariate Regression
Nonlinear Correlation and Regression
Multiple Linear Correlation and Regression Analysis
Problems for Discussion and Solutions
12 MULTIVARIATE ANALYSIS
Types of Multivariate Analyses
Multivariate Analysis by Principal Components
Multivariate Factor Analysis
Multivariate Canonical Analysis
Problems for Discussion
REFERENCES
INDEX
|
