CAJ | 학술논문

阐明了将检测两子样本平均值之差的学生氏t检验推广到对多尺度突变现象进行扫描式检测的计算方法；对于t检验要求序列独立的限制，引用了初步的订正方法；还给出了检测两个序列间多尺度突变相干性的计算公式.扫描式t检验不仅具有相当于子波变换检测多尺度突变现象的功能，而且解决了子波变换检测突变时缺少临界值的问题.由于t统计量包含有二阶矩均方差，它不能像子波变换那样作为分解工具，但检测的尺度参数也就不必局限于2的整数幂，因而可以进行扫描式检测.应用于尼罗河年最高与最低水位历史序列(AD622—1470)，能较客观和精确地检测出两序列在某些尺度上的相干性(同步或反位相)变化；并由此重新划分了该流域几十年至百余年时间尺度的相对干湿期.结果与目前查阅到的埃及灾荒历史记载相吻合.
천명료장검측량자양본평균치지차적학생씨t검험추엄도대다척도돌변현상진행소묘식검측적계산방법；대우t검험요구서렬독립적한제，인용료초보적정정방법；환급출료검측량개서렬간다척도돌변상간성적계산공식.소묘식t검험불부구유상당우자파변환검측다척도돌변현상적공능，이차해결료자파변환검측돌변시결소림계치적문제.유우t통계량포함유이계구균방차，타불능상자파변환나양작위분해공구，단검측적척도삼수야취불필국한우2적정수멱，인이가이진행소묘식검측.응용우니라하년최고여최저수위역사서렬(AD622—1470)，능교객관화정학지검측출량서렬재모사척도상적상간성(동보혹반위상)변화；병유차중신화분료해류역궤십년지백여년시간척도적상대간습기.결과여목전사열도적애급재황역사기재상문합.
A scanning t test of multi-scale abrupt changes is introduced byextending the student t test,which detects the difference between two subsample means. It is shown that this algorithm has not only the capacity similar to Haar wavelet transform coefficient W(a,b) for detection of multi-scale abrupt changes,but also gives the statistic significance threshold,which the wavelet analysis can not do. The subsample size n (comparative to the scale parameter a in W(a,b)) of the statistic t(n,j) may vary successively without limitation of integer power of 2 as in the wavelet transform for a discrete series,so that the algorithm may detect any longer signal series like a scanner. However,this algorithm is not a decomposition tool because the second momentum,the variance,is involved. In addition,a correction to the Effective Degrees of Freedom (Ef) of t test is adopted for the dependency of an observation series to be detected. A coherence detection of abrupt changes between two signal series is carried out. The results of an application to historic series (AD622-1470) of the maximum and minimum flood levels of the Nile River reveal objectively that there appears some abrupt changes in phase and out of phase on certain scales between the two series. The relative dry and wet phases on around 0.5—1.5 century scale are further repartitioned following this detection. And these dry/wet phases coincide better with historic records of catastrophe in Egypt found so far and are some improvements upon previous researches.