Fitting log normal distributions to hydrologic data

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Abstract
The mean square error of estimation of selected quantities is used to evaluate the efficiency of alternative methods for fitting the two‐ and three‐parameter log normal distributions. Monte Carlo results show that use of maximum likelihood parameter estimation dominates other methods for fitting the two‐parameter log normal distribution for samples of 25 or more log normal variates. For the three‐parameter log normal distribution the standard moment method performs best for log normal distributions with low skew coefficients, while use of the sample mean, variance, and quantile estimate of the lower bound performs better for highly skewed log normal distributions; use of the unbiased standard deviation and skew coefficient is almost dominated by this new fitting procedure. The performance of the better fitting procedures is also evaluated when the observations are drawn from a log Pearson type 3 distribution.