A three-parameter log-normal distribution is derived as an exact functional transform of an embedded normal distribution. The parameters of this function are evaluated by fitting to histograms of natural hydrologic data. The practice of transformation of data is made unnecessary and can be eliminated. Tolerance limits of extreme hydrologic events can be calculated as transforms of the exact tolerance limits of the embedded normal, permitting precise probabilistic statements on such statistics as T-year floods or droughts.

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