Book contents
- Systems of Frequency Distributions for Water and Environmental Engineering
- Systems of Frequency Distributions for Water and Environmental Engineering
- Copyright page
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Pearson System of Frequency Distributions
- 3 Burr System of Frequency Distributions
- 4 D’Addario System of Frequency Distributions
- 5 Dagum System of Frequency Distributions
- 6 Stoppa System of Frequency Distributions
- 7 Esteban System of Frequency Distributions
- 8 Singh System of Frequency Distributions
- 9 Systems of Frequency Distributions Using Bessel Functions and Cumulants
- 10 Frequency Distributions by Entropy Maximization
- 11 Transformations for Frequency Distributions
- 12 Genetic Theory of Frequency
- Appendix Datasets for Applications
- Index
- References
10 - Frequency Distributions by Entropy Maximization
Published online by Cambridge University Press: 06 November 2020
Book contents
- Systems of Frequency Distributions for Water and Environmental Engineering
- Systems of Frequency Distributions for Water and Environmental Engineering
- Copyright page
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Pearson System of Frequency Distributions
- 3 Burr System of Frequency Distributions
- 4 D’Addario System of Frequency Distributions
- 5 Dagum System of Frequency Distributions
- 6 Stoppa System of Frequency Distributions
- 7 Esteban System of Frequency Distributions
- 8 Singh System of Frequency Distributions
- 9 Systems of Frequency Distributions Using Bessel Functions and Cumulants
- 10 Frequency Distributions by Entropy Maximization
- 11 Transformations for Frequency Distributions
- 12 Genetic Theory of Frequency
- Appendix Datasets for Applications
- Index
- References
Summary
A wide spectrum of frequency distributions that are commonly used in hydrologic, hydraulic, environmental and water resources engineering can be derived by employing the principle of maximum entropy. Entropy maximization provides a general framework for deriving any probability distribution subject to appropriate constraints. This chapter discusses this framework and derives a number of distributions which satisfy different constraints.
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2020
References
Shannon, E. E. (1948). A mathematical theory of communication. Bell System Technical Journal 27(3). doi: 10.1002/j.1538-7305.1948.tb01338.x.CrossRefGoogle Scholar
Singh, V. P. (1997). Entropy-Based Parameter Estimation in Hydrology. Dordrecht: Springer.Google Scholar
Singh, V. P., and Rajagopal, A. K. (1986). A new method of parameter estimation for hydrologic frequency analysis. Hydrological Science and Technology 2, no. 3, pp. 33‒40.Google Scholar
Singh, V. P., Rajagopal, A. K., and Singh, K. (1985). Derivation of some frequency distributions using principle of maximum entropy (POME). Advances in Water Resources 9, pp. 91‒106.CrossRefGoogle Scholar