基于偏态分布的百分位估计公式的建立

Development of percentile estimation formula for skewed distribution

顺序统计量将累积概率与数据排序后的位置建立相关联系,可用于估计数据分布的累积概率.鉴于不同气候要素概率分布存在着不同程度的偏态特征,基于偏态分布条件下的累积概率函数,通过理论推导和数值模拟建立了与偏态指数相关的位置参数的回归模型,从而给出了基于数据偏态特征的经验百分位估计公式.利用1980年—2009年全球夏季逐日平均温度资料,进一步对比分析了偏态百分位估计方法与Jenkinson方法下得到的第90个百分位值所对应的温度排序后位置的差异.

Order statistics establishes a relation between the position of the ranked data and corresponding cumulative probability,so it can be used to estimate the cumulative probability.Owing to the fact that different climatological data have different skewness degrees,in this paper,according to the cumulative probability function under the skewed distribution conditions,we perform theoretical analysis and numerical simulation to establish the position parameters of the regression model which are related to skewness index,then give an amperic percentile formula under the skewed distribution.By using the data about the summer temperature in global from 1980 to 2009,we compare the positions of ranked data corresponding to the 90th percentile,which are obtained by this formula and Jenkinson＇s formula.