Probability and Statistics in Hydrology, 1972, 2010
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Photograph
Authors
Editions, Dates
1972 Reprint Edition 2010
Publisher, Place
Water Resource Publications, Highlands Ranch, Colorado, USA
ISBN
ISBN-13: 978-1887201605 (Reprint Edition, 2010)
Contents
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
- 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
- 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
- Descriptors of Distributions of Bivariates, Multivariates, and Conditional Variables
- 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
