随机信息中正态总体方差的灰色统计假设检验研究

Normal variance gray statistical hypothesis testing on random information

根据灰色系统理论，利用样本的白化权函数，构建了正态方差的灰色检验统计量W=n-1/σo2σ2，并计算出其α截集W[α] ，在此基础上确定了灰色检验统计量 的临界值灰数GS1和GS2及其α截集GS1[α]和GS2[α]。然后根据灰数比较大小的方法，将W与其临界值GS1和GS2进行比较，得到了正态方差的灰色统计假设检验判定方法：若W〉GS2或 〈GS1，拒绝原假设H0；若GS1〈W〈GS2，则接受原假设H0；若GS1〈W≈GS2、GS1≈W〈GS2、GS1≈W≈GS2则无法判断，从而建立了随机信息中正态总体方差的灰色统计假设检验方法，并通过实例检验。表明正态总体方差的灰色统计假设检验比经典N-P假设检验更具有效性和合理性。从而实现了利用灰色系统理论，将经典统计学的理论拓广到具有灰色性的不确定性数据。

According to the theory of gray system, using the whiting values t function of sample, this paper constructed the Gray test statistic W=n-1/σo2σ2 of normal variance, calculated the a cut set W[ α] .On this basis, the critical value GS1 and GS2 of gray test statistics Wwas determined, and the a cut set GS1 [ α ] and GS2 [ α ] was calculated. Then according to the method of gray hum-ber comparison,let Wand their critical value GS1 [ α ] and GS2 [ α ] comparison, this paper got the gray statistical hypothesis tes-ting of normal variance method： If W 〉 GS2 orlW〈 GS1 ,the null hypothesis H0 is rejected ;if GS1 〈 W 〈 GS2 ,then the null hypothesisHo is accepted; if GS1〈W≈GS2、GS1≈W〈GS2、GS1≈W≈GS2 , then they can not be judged. Thus in therandom information, gray statistics normal variance method of hypothesis test was established. And comparison through the N - P hypothesis testing methods and classic examples was made, which showed that the gray statistical normal variance hypothesis test method can provide more effective irfformation, illustrates the validity and reality of gray statistics normal variance method of hy- pothesis test, so as to realize the use of gray system theory, and the classical statistical theory was extended to the uncertain data with gray.