基于Beta分布形状的拟合优度检验

Powerful Modified-EDF Goodness-of-fit Test Based On Skewness and Kurtosis Analysis

本文指出了拟合优度检验中选用经验频率公式时存在的误区,对顺序统计量失效概率分布进行了偏态和峰态分析,提出了一个基于Beta分布形状特征的经验分布函数,给出了精确值和近似值两种计算方法,在此基础上建立新的极值型检验统计量．利用Monte Carlo方法进行数值模拟,得到0．01、0．05、0．1显著度水平下检验统计量的临界值,并利用常用的分布模型进行检验功效比较,数值模拟结果表明基于分布形状的经验频率公式能更好地反映顺序统计量失效概率分布的集中趋势,证明了本文提出的两种检验统计量在中小样本条件下具有更优的检验功效．

The existing attitude that the criterion for choice of frequency function in Empirical distribution function （EDF） goodness-of-fit（GOF） tests is arbitrary is rebuked. This paper analyzes the skewness and kurtosis characteristics of the failure probability distribution of order statistics, and then proposes a worthwhile frequency function based on Beta-distribution. For practical application purposes, a simple approximate formula is also introduced. Additionally, new modified-EDF test statistics are constructed based on the extreme discrepancy criterion. Monte Carlo method is employed to obtain the critical values corresponding to 0.01, 0.05 and 0.1 significance levels and to conduct test power comparisons. The results of numerical examples demonstrate the advantages related to the use of these two suggested modified-EDF GOF tests especially for data of small and moderate sample sizes.