P-Ⅲ型分布次序统计量期望值数值计算

A Numerical Arithmetric for Computing Expected Values of Pearson Type-in Order Statistics

本文探讨了P-Ⅲ型(皮尔逊Ⅲ型)分布次序统计量期望值数值计算的公式、数值计算的精度控 制等问题,在此基础上提出了P-Ⅲ型分布次序统计量期望值的数值计算框架。经检验,该计算框架突破了 以往次序统计量期望值数值计算的瓶颈,样本长度和数值计算精度均满足科研和生产实践的要求。

This paper explored the calculation formulas and the accuracy controlling of computing expected values of order statistics, and a numerical arithmetric for computing expected values of Pearson type-Ⅲ order statistics was presented. The application has shown that the establishment of the arithmetic would break the bottleneck of the calculation for estimating the expected values of order statistics, such as the limitation on sample sizes and tile calculation accuracy. The results have also shown that tile new numerical arithmetic with large sample size （1000） and wider range of the skewness values of the distribution can be applied both on the science research and operational practice.