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
5 - Halphen Inverse B 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 Halphen type inverse B (Hal-IB) distribution is obtained from the Halphen type B distribution. This chapter discusses the derivation of the Hal-IB distribution and its characteristics and the estimation of its parameters using the methods of maximum entropy, moments, and maximum likelihood.
- Type
- Chapter
- Information
- Publisher: Cambridge University PressPrint publication year: 2022
References
Perreault, L., Bobée, B., and Rasmussen, P. (1999). Halphen distribution system. I: Mathematical and statistical properties. Journal of Hydrologic Engineering, Vol. 4, No. 3, pp. 189–199.Google Scholar
Shannon, C.E. (1948). A mathematical theory of communication. Bell System Technical Journal, Vol. 27, No. 3, pp. 379–423.CrossRefGoogle Scholar
Singh, V.P. (2011). Hydrologic synthesis using entropy theory: Review. Journal of Hydrologic Engineering, Vol. 16, No. 5, pp. 421–433.CrossRefGoogle Scholar
Singh, V.P. (2013). Entropy Theory and Its Application in Environmental and Water Engineering. Wiley-Blackwell, Hoboken, NJ.Google Scholar