Book contents
- Generalized Frequency Distributions for Environmental and Water Engineering
- Generalized Frequency Distributions for Environmental and Water Engineering
- Copyright page
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Burr–Singh–Maddala Distribution
- 3 Halphen Type A Distribution
- 4 Halphen Type B Distribution
- 5 Halphen Inverse B Distribution
- 6 Three-Parameter Generalized Gamma Distribution
- 7 Generalized Beta Lomax Distribution
- 8 Feller–Pareto Distribution
- 9 Kappa Distribution
- 10 Four-Parameter Exponential Gamma Distribution
- 11 Summary
- Appendix General Procedure for Goodness-of-Fit Study, Construction of Confidence Interval, and 95% Confidence Bound with Parametric Bootstrap Method
- Index
- References
8 - Feller–Pareto Distribution
Published online by Cambridge University Press: 13 April 2022
Book contents
- Generalized Frequency Distributions for Environmental and Water Engineering
- Generalized Frequency Distributions for Environmental and Water Engineering
- Copyright page
- Dedication
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Burr–Singh–Maddala Distribution
- 3 Halphen Type A Distribution
- 4 Halphen Type B Distribution
- 5 Halphen Inverse B Distribution
- 6 Three-Parameter Generalized Gamma Distribution
- 7 Generalized Beta Lomax Distribution
- 8 Feller–Pareto Distribution
- 9 Kappa Distribution
- 10 Four-Parameter Exponential Gamma Distribution
- 11 Summary
- Appendix General Procedure for Goodness-of-Fit Study, Construction of Confidence Interval, and 95% Confidence Bound with Parametric Bootstrap Method
- Index
- References
Summary
The five-parameter Feller–Pareto distribution may be considered as a generalization of the two-parameter beta distribution through transformation. In this chapter, the five-parameter Feller–Pareto distribution is derived using entropy theory and then its parameters are estimated with the principle of maximum entropy and the methods of maximum likelihood estimation and moments. Synthetic data from true population and real-world data including peak flow, maximum daily precipitation, and total flow deficit are applied to evaluate the performance of different estimation methods.
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2022
References
Arnold, B.C. (1983). Pareto Distributions. International Cooperative Publishing House, Fairland, MD.Google Scholar
Klugman, S.A., Panjer, H.H., and Wilmot, G.E. (1998). Loss Model: From Data to Decision. Wiley, New York.Google Scholar
Mahmoud, M.R. and Abd El Ghafour, A.S. (2013). Shannon entropy for the generalized Feller–Pareto (GFP) family and order statistics of the GFP subfamilies. Applied Mathematical Sciences, Vol. 7, No. 65, pp. 3247–3253.CrossRefGoogle Scholar