%0 Journal Article
%A HU Shi-song
%A CHEN Jin
%A YIN Zheng-jie
%T Maximum Likelihood Estimation of Negative-skewness Hydrological Series
%D 2015
%R 10.3969/j.issn.1001-5485.2015.06.020
%J Journal of Yangtze River Scientific Research Institute
%P 116-119
%V 32
%N 6
%X The commonly used probability density function of Pearson-III distribution is invalid for negative-skewness water level and tide level series (<i>β</i>&lt;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  <i>ξ</i> is decided by the negative-skewness distribution and the MLE of  <i>α</i> and <i>β</i>   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.
%U http://ckyyb.crsri.cn/EN/10.3969/j.issn.1001-5485.2015.06.020