Ebook: Entropy-Based Parameter Estimation in Hydrology

Since the pioneering work of Shannon in the late 1940's on the development of the theory of entropy and the landmark contributions of Jaynes a decade later leading to the development of the principle of maximum entropy (POME), the concept of entropy has been increasingly applied in a wide spectrum of areas, including chemistry, electronics and communications engineering, data acquisition and storage and retreival, data monitoring network design, ecology, economics, environmental engineering, earth sciences, fluid mechanics, genetics, geology, geomorphology, geophysics, geotechnical engineering, hydraulics, hydrology, image processing, management sciences, operations research, pattern recognition and identification, photogrammetry, psychology, physics and quantum mechanics, reliability analysis, reservoir engineering, statistical mechanics, thermodynamics, topology, transportation engineering, turbulence modeling, and so on. New areas finding application of entropy have since continued to unfold. The entropy concept is indeed versatile and its applicability widespread. In the area of hydrology and water resources, a range of applications of entropy have been reported during the past three decades or so. This book focuses on parameter estimation using entropy for a number of distributions frequently used in hydrology. In the entropy-based parameter estimation the distribution parameters are expressed in terms of the given information, called constraints. Thus, the method lends itself to a physical interpretation of the parameters. Because the information to be specified usually constitutes sufficient statistics for the distribution under consideration, the entropy method provides a quantitative way to express the information contained in the distribution.

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The book covers entropy-based techniques for parameter estimation in hydrology. The techniques are presented for twenty distributions used in hydrology, including the distributions of the normal family, the extreme-value family, the Pareto family, and the logistic family. A comparative assessment of the entropy-based techniques is made with traditional methods of parameter estimation, such as the methods of moments, maximum likelihood estimation, probability-weighted moments, L-moments, and least squares, using field data as well as Monte Carlo simulation experiments.
The book is the first attempt to comprehensively present the entropy-based techniques for most distributions of interest in hydrology.
Audience: The material covered in the book will be of interest to graduate students, researchers, and teachers, as well as practitioners of agricultural engineering, civil engineering, agricultural sciences, earth sciences, environmental sciences, and forest and range sciences.

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The book covers entropy-based techniques for parameter estimation in hydrology. The techniques are presented for twenty distributions used in hydrology, including the distributions of the normal family, the extreme-value family, the Pareto family, and the logistic family. A comparative assessment of the entropy-based techniques is made with traditional methods of parameter estimation, such as the methods of moments, maximum likelihood estimation, probability-weighted moments, L-moments, and least squares, using field data as well as Monte Carlo simulation experiments.
The book is the first attempt to comprehensively present the entropy-based techniques for most distributions of interest in hydrology.
Audience: The material covered in the book will be of interest to graduate students, researchers, and teachers, as well as practitioners of agricultural engineering, civil engineering, agricultural sciences, earth sciences, environmental sciences, and forest and range sciences.
Content:
Front Matter....Pages i-xv
Entropy and Principle of Maximum Entropy....Pages 1-11
Methods of Parameter Estimation....Pages 12-44
Uniform Distribution....Pages 45-48
Exponential Distribution....Pages 49-55
Normal Distribution....Pages 56-67
Two-Parameter Lognormal Distribution....Pages 68-81
Three-Parameter Lognormal Distribution....Pages 82-107
Extreme Value Type 1 Distribution....Pages 108-136
Log-Extreme Value Type 1 Distribution....Pages 137-149
Extreme Value Type III Distribution....Pages 150-168
Generalized Extreme Value Distribution....Pages 169-183
Weibull Distribution....Pages 184-201
Gamma Distribution....Pages 202-230
Pearson Type III Distribution....Pages 231-251
Log-Pearson Type III Distribution....Pages 252-274
Beta Distribution....Pages 275-283
Two-Parameter Log-Logistic Distribution....Pages 284-296
Three-Parameter Log-Logistic Distribution....Pages 297-311
Two-Parameter Pareto Distribution....Pages 312-323
Two-Parameter Generalized Pareto Distribution....Pages 324-335
Three-Parameter Generalized Pareto Distribution....Pages 336-346
Two-Component Extreme Value Distribution....Pages 347-362
Back Matter....Pages 363-368

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The book covers entropy-based techniques for parameter estimation in hydrology. The techniques are presented for twenty distributions used in hydrology, including the distributions of the normal family, the extreme-value family, the Pareto family, and the logistic family. A comparative assessment of the entropy-based techniques is made with traditional methods of parameter estimation, such as the methods of moments, maximum likelihood estimation, probability-weighted moments, L-moments, and least squares, using field data as well as Monte Carlo simulation experiments.
The book is the first attempt to comprehensively present the entropy-based techniques for most distributions of interest in hydrology.
Audience: The material covered in the book will be of interest to graduate students, researchers, and teachers, as well as practitioners of agricultural engineering, civil engineering, agricultural sciences, earth sciences, environmental sciences, and forest and range sciences.
Content:
Front Matter....Pages i-xv
Entropy and Principle of Maximum Entropy....Pages 1-11
Methods of Parameter Estimation....Pages 12-44
Uniform Distribution....Pages 45-48
Exponential Distribution....Pages 49-55
Normal Distribution....Pages 56-67
Two-Parameter Lognormal Distribution....Pages 68-81
Three-Parameter Lognormal Distribution....Pages 82-107
Extreme Value Type 1 Distribution....Pages 108-136
Log-Extreme Value Type 1 Distribution....Pages 137-149
Extreme Value Type III Distribution....Pages 150-168
Generalized Extreme Value Distribution....Pages 169-183
Weibull Distribution....Pages 184-201
Gamma Distribution....Pages 202-230
Pearson Type III Distribution....Pages 231-251
Log-Pearson Type III Distribution....Pages 252-274
Beta Distribution....Pages 275-283
Two-Parameter Log-Logistic Distribution....Pages 284-296
Three-Parameter Log-Logistic Distribution....Pages 297-311
Two-Parameter Pareto Distribution....Pages 312-323
Two-Parameter Generalized Pareto Distribution....Pages 324-335
Three-Parameter Generalized Pareto Distribution....Pages 336-346
Two-Component Extreme Value Distribution....Pages 347-362
Back Matter....Pages 363-368
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