Estimation of Pearson type 3 moments

Estimates of frequencies of floods and other events are based on statistical distributions estimated from sample data. The most common and generally the most robust technique used is the fitting of data by the method of moments. It is well known that moments of the data of an order higher than 1 are biased estimates of the moments of the population from which the data represent a sample. Much work has been done in deriving factors or functions by which the bias can be corrected. All of such work has been based on considering the variation of statistics of various samples drawn from a specified population, whereas the real interest is in the range of likely parent population parameters corresponding to a statistic obtained from a unique sample. It is recognized that there is no solution to this problem without an assumption of the range and distribution of such parameters as they occur in nature. The study described herein examines this question with regard to a particular functional form of parent distribution and for the case where the a priori distributions of the parameters are uniform, that is, where all values of a particular parameter are equally likely on an arithmetic scale. The distribution function studied is the Pearson type 3, and the parameter of primary attention is the skew coefficient.