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Systems of frequency distributions for water and environmental engineering

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  • Singh, Vijay P.

Abstract

A wide spectrum of frequency distributions are used in hydrologic, hydraulic, environmental and water resources engineering. These distributions may have different origins, are based on different hypotheses, and belong to different generating systems. Review of literature suggests that different systems of frequency distributions employed in science and engineering in general and environmental and water engineering in particular have been derived using different approaches which include (1) differential equations, (2) distribution elasticity, (3) genetic theory, (4) generating functions, (5) transformations, (6) Bessel function, (7) expansions, and (8) entropy maximization. This paper revisits these systems of distributions and discusses the hypotheses that are used for deriving these systems. It also proposes, based on empirical evidence, another general system of distributions and derives a number of distributions from this general system that are used in environmental and water engineering.

Suggested Citation

  • Singh, Vijay P., 2018. "Systems of frequency distributions for water and environmental engineering," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 50-74.
    • Handle: RePEc:eee:phsmap:v:506:y:2018:i:c:p:50-74
    DOI: 10.1016/j.physa.2018.03.038
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    1. Paranaíba, Patrícia F. & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R., 2011. "The beta Burr XII distribution with application to lifetime data," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1118-1136, February.
    2. Singh, S K & Maddala, G S, 1976. "A Function for Size Distribution of Incomes," Econometrica, Econometric Society, vol. 44(5), pages 963-970, September.
    3. James B. McDonald, 2008. "Some Generalized Functions for the Size Distribution of Income," Economic Studies in Inequality, Social Exclusion, and Well-Being, in: Duangkamon Chotikapanich (ed.), Modeling Income Distributions and Lorenz Curves, chapter 3, pages 37-55, Springer.
    4. Majumder, Amita & Chakravarty, Satya Ranjan, 1990. "Distribution of Personal Income: Development of a New Model and Its Application to U.S. Income Data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 189-196, April-Jun.
    5. Salem, A B Z & Mount, T D, 1974. "A Convenient Descriptive Model of Income Distribution: The Gamma Density," Econometrica, Econometric Society, vol. 42(6), pages 1115-1127, November.
    6. Hogg, Robert V. & Klugman, Stuart A., 1983. "On the estimation of long tailed skewed distributions with actuarial applications," Journal of Econometrics, Elsevier, vol. 23(1), pages 91-102, September.
    7. Kloek, Teun & van Dijk, Herman K., 1978. "Efficient estimation of income distribution parameters," Journal of Econometrics, Elsevier, vol. 8(1), pages 61-74, August.
    8. McDonald, James B & Butler, Richard J, 1987. "Some Generalized Mixture Distributions with an Application to Unemployment Duration," The Review of Economics and Statistics, MIT Press, vol. 69(2), pages 232-240, May.
    9. Thurow, Lester C, 1970. "Analyzing the American Income Distribution," American Economic Review, American Economic Association, vol. 60(2), pages 261-269, May.
    10. Cronin, D C, 1979. "Function for Size Distribution of Incomes: A Further Comment," Econometrica, Econometric Society, vol. 47(3), pages 773-774, May.
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    Cited by:

    1. Roy, Sanjoy, 2019. "Run-of-river hydro generation in presence of sub-daily source flow variations," Energy, Elsevier, vol. 172(C), pages 1268-1276.

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