Generalized frequency distributions for environmental and water engineering /
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| Author / Creator: | Singh, V. P. (Vijay P.), author. |
|---|---|
| Imprint: | Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2022. ©2022 |
| Description: | 1 online resource ( xvi, 315 pages) : illustrations |
| Language: | English |
| Subject: | |
| Format: | E-Resource Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/13118565 |
Table of Contents:
- Cover
- Half-title page
- Title page
- Copyright information page
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 1.1 Introduction
- 1.2 Generalized Distributions
- 1.3 Distribution Characteristics
- 1.4 Characterization through Hazard Function
- 1.4.1 Gamma Distribution
- 1.4.2 Weibull Distribution
- 1.4.3 Modified Extreme Value Distribution
- 1.4.4 Pareto Distribution
- 1.4.5 Lognormal Distribution
- 1.4.6 Log-Logistic Distribution
- 1.5 Methods of Parameter Estimation
- 1.5.1 Regular Entropy Method
- 1.5.2 Parameter Space Expansion Method
- 1.5.3 MOM
- 1.5.4 Method of PWMs
- 1.5.5 Method of L-Moments
- 1.5.6 MLE Method
- 1.5.7 Method of Cumulative Moments
- 1.5.8 Least Squares Method
- 1.6 Selection of a Distribution
- 1.7 Goodness-of-Fit Measures
- References
- 2 Burr-Singh-Maddala Distribution
- 2.1 Introduction
- 2.2 Characteristics of BSM Distribution
- 2.3 Characterization through Hazard Function
- 2.4 Derivation of BSM Distribution
- 2.4.1 Singh-Maddala Method
- 2.4.2 Another Singh-Maddala Method
- 2.4.3 Differential Equation Method
- 2.4.4 Entropy Method
- 2.5 Parameter Estimation
- 2.5.1 Regular Entropy Method
- 2.5.2 Parameter Space Expansion Method
- 2.5.2.1 Derivation of Entropy Function
- 2.5.2.2 Relation between Parameters and Constraints
- 2.5.3 Method of Moments
- 2.5.4 Maximum Likelihood Estimation Method
- 2.5.5 Probability Weighted Moments Method
- 2.5.6 Method of L-Moments
- 2.5.7 Method of Cumulative Moments
- 2.6 Application
- 2.6.1 Synthetic Data
- 2.6.2 Peak Flow
- 2.6.3 Maximum Daily Precipitation
- 2.6.4 Drought (Total Flow Deficit)
- 2.7 Conclusion
- References
- 3 Halphen Type A Distribution
- 3.1 Introduction
- 3.2 Hal-A Distribution and Its Characteristics
- 3.3 Differential Equation for Derivation of Hal-A Distribution
- 3.4 Derivation of Hal-A Distribution by Entropy Theory
- 3.4.1 Specification of Constraints
- 3.4.2 Entropy Maximizing
- 3.4.3 Relation between Lagrange Multipliers and Distribution Parameters
- 3.5 Parameter Estimation
- 3.5.1 Regular Entropy Method
- 3.5.1.1 Relations between Lagrange Multipliers and Constraints
- 3.5.2 Parameter Space Expansion Method
- 3.5.3 MOM
- 3.5.4 MLE Method
- 3.6 Application
- 3.6.1 Simulating Hal-A Distributed Random Variable with Fixed Parameters
- 3.6.2 Parameter Estimation Using Simulated Random Variables
- 3.6.3 Peak Flow
- 3.6.4 Total Flow Deficit
- 3.6.5 Maximum Daily Precipitation
- 3.7 Conclusion
- References
- 4 Halphen Type B Distribution
- 4.1 Introduction
- 4.2 Hal-B Distribution and Its Characteristics
- 4.3 Differential Equation for Hal-B Distribution and Distribution Characteristics
- 4.4 Derivation of Hal-B Distribution by Entropy Theory
- 4.4.1 Specification of Constraints
- 4.4.2 Entropy Maximizing
