Abstract: The commonly used probability density function of Pearson-III distribution is invalid for negative-skewness water level and tide level series (β<0). To solve this problem, a means of maximum likelihood estimation (MLE) based on the relationship between negative-skewness series and positive-skewness series is proposed. In this method negative-skewness Pearson-Ⅲ distribution is translated into positive-skewness Pearson-Ⅲ and gamma distribution in sequence. The initial value of ξ is decided by the negative-skewness distribution and the MLE of α and β are calculated through the gamma distribution. In the iterative process the sampling error with evaluating coefficient of skewness will be avoided. Moreover, the 44-year record of maximum tide level at a tide station is used as calculation example. The fitting accuracy of negative-skewness MLE, negative-skewness moment method and positive-skewness table look-up are compared. The fitting results of negative-skewness MLE (test value of PPCC is 0.993, OLS 0.010, and KS 0.052) are superior to those of the other two methods. In conclusion, negative-skewness MLE has the optimum fitting accuracy for negative-skewness hydrological series.

Key words: hydrological frequency, negative-skewness series, MLE, Pearson-Ⅲ frequency curve, MATLAB software