Probability and Statistics in Hydrology, 1972, 2010

Photograph

Authors

Yevjevich, Vujica M.

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

Links

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