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Gamma Distribution

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Book cover Entropy-Based Parameter Estimation in Hydrology

Part of the book series: Water Science and Technology Library ((WSTL,volume 30))

Abstract

The two-parameter gamma distribution is commonly employed for synthesis of instantaneous or finite-period unit hydrographs (Dooge, 1973) and also for flood frequency analysis (Haan, 1977; Phien and Jivajirajah, 1984; Yevjevich and Obseysekera, 1984). By making two hydrologic postulates, Edson (1951) was perhaps the first to derive it for describing a unit hydrograph (UH). Using the theory of linear systems Nash (1957, 1959, 1960) showed that the mathematical equation of the instantaneous unit hydrograph (IUH) of a basin represented by a cascade of equal linear reservoirs would be a gamma distribution. This also resulted as a special case of the general unit hydrograph theory developed by Dooge (1959). On the other hand, using statistical and mathematical reasoning, Lienhard and associates (Lienhard, 1964; Lienhard and Davis, 1971; Lienhard and Meyer, 1967) derived this distribution as a basis for describing the IUH. Thus, these investigators laid the foundation of a hydrophysical basis underlying the use of this distribution in synthesizing the direct runoff. There has since been a plethora of studies employing this distribution in surface water hydrology (Gray, 1961; Wu, 1963; DeCoursey, 1966; Dooge, 1973; Gupta and Moin, 1974; Gupta, et al., 1974; Croley, 1980; Aron and White, 1982; Singh, 1982a, 1982b, 1988; Collins, 1983).

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Authors and Affiliations

  1. Water Resources Program, Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, USA

    Vijay P. Singh

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Singh, V.P. (1998). Gamma Distribution. In: Entropy-Based Parameter Estimation in Hydrology. Water Science and Technology Library, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1431-0_13

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  • DOI: https://doi.org/10.1007/978-94-017-1431-0_13

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  • Online ISBN: 978-94-017-1431-0

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