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The 3-Parameter Lognormal Distribution and Its Applications in Hydrology

The 3-parameter lognormal distribution is a general skew distribution in which the logarithm of any linear function of a given variable is normally distributed. The distribution is applied to the frequency analysis of floods, annual flows, and monthly flows, and a comparison with other commonly used methods suggests that it can be successfully used for this purpose. A procedure for its application has been suggested using only the median, the mean, and the standard deviation of the original data. The Gumbel distribution is a special case, and any straight line on the Gumbel probability paper can be transformed into a straight line on the lognormal probability paper by the 3-parameter lognormal distribution. The sample of 10 stations used in this study all exhibited negative skewness for the logarithms of the data and therefore the lognormal distribution that assumes this skewness equal to zero has generally given high estimates.

B. P. Sangal and Asit K. Biswas, 1970, Water Resources Research, Volume 6, Number 2, pages 505,-515

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