Abstract
The extreme value type 1 (EV 1) distribution is one of the most popularly used distributions for frequency analysis of extreme values of meteorologic or climatic and hydrologic variables, such as floods, rainfall, droughts, etc. This distribution was derived by Fisher and Tippett (1928) as a limiting form of the frequency distribution of the largest or smallest of a sample. In a series of papers Gumbel (1941a, b, 1942a, b, 1948) derived the EV1 distribution for flood flows and applied it to frequency analysis of floods, droughts, and meteorological data. Gumbel (1958) published a treatise on statistics of extremes, which contains a comprehensive treatment of EV1 distribution. Bardsley and Manly (1987) examined the transformations under which non-Gumbel distributions of annual flood flow maxima would converge to the Gumbel distribution. Smith (1986) presented a family of statistical distributions and estimators based on a fixed number (greater than one) of the largest annual events. Jenkinson (1955) found a general solution of the function equation derived by Fisher and Tippett (1928) for extreme values and showed that the Gumbel distribution was a special case of the general solution. Singh et al. (1986) derived this distribution using the principle of maximum entropy. Al-Mashidini et al. (1978) presented a simplified form of EV 1 distribution for flood estimation.
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Singh, V.P. (1998). Extreme Value Type 1 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_8
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