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
8 - Singh System of Frequency Distributions
Published online by Cambridge University Press: 06 November 2020
- 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
There are many frequency distributions whose cumulative distribution functions (CDFs) cannot be expressed in closed form. Examples of such distributions are normal, lognormal, gamma, Pearson type III, among others. If a distribution has a closed form CDF then its probability density function (PDF) can be easily obtained by differentiation but vice versa is not tractable. Using certain hypotheses on the relation between PDF and CDF based on empirical data, the CDFs of a large number of distributions can be derived. This chapter discusses the derivation of CDFs of such distributions many of which are frequently used in hydrologic, hydraulic, environmental, and water resources engineering.
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- Publisher: Cambridge University PressPrint publication year: 2020