一:步骤解说:
1、排列数据 Collections.sort(dataArrayList);
2、求平均值、标准差
3、计算Gi值:每个数据与平均数的残差 / 标准差
4、用这个Gi 值 与 格拉布斯临界表表中的 临界值比较,越大,越异常,需剔除
注:
- 这个临界值 与 顶尖水平(alpha)有关 在0.01 - 0.99中选,越小越严格 ,以及测量次数(数组集合长度)
- 查格拉布斯表获得临界值: 根据 置信概率(1-alpha) 和测验次数 横纵交得临界值
代码
import java.util.ArrayList;
import java.util.Collections;
import java.util.Iterator;
import java.util.List;
public class Truncat {
private ArrayList<Double> dataArrayList;
private int length;
private final double alpha = 0.05;
//传入一组数据,我们要做的是剔除最大或最小的异常值
public Truncat(ArrayList<Double> arrayList) {
this.dataArrayList = arrayList;
this.length = arrayList.size();
}
public ArrayList<Double> calc() {
//因为格拉布斯准则只能对大于等于3个数据进行判断,所以数据量小于3时,直接返回
if (dataArrayList.size() < 3) {
return dataArrayList;
}
//首先对数据进行排序
Collections.sort(dataArrayList);
//求出数据平均值和标准差
double average = calcAverage(dataArrayList);
double standard = calcStandard(dataArrayList, length, average);
// 循环取每个数据和平均数据的标准差,过了就剔除!
Iterator<Double> it = dataArrayList.iterator();
while(it.hasNext()){
Double item = it.next();
//与平均值之差
double diffAvg = (item>average)?(item-average):(average-item);
//差值/标准差
double waveValue = diffAvg/standard;//波动
//做比较,是否剔除
if (waveValue > calcG(alpha, length)) {
it.remove();
}
}
return dataArrayList;
}
//求平均
public double calcAverage(ArrayList<Double> sample) {
double sum = 0;
int cnt = 0;
for (int i = 0; i < sample.size(); i++) {
sum += sample.get(i);
cnt++;
}
return (double) sum / cnt;
}
//求标准差
private double calcStandard(ArrayList<Double> array, int n, double average) {
double sum = 0;
for (int i = 0; i < n; i++) {
sum += ((double) array.get(i) - average)
* ((double) array.get(i) - average);
}
return (double) Math.sqrt((sum / (n - 1)));
}
//算临界值的表,这里alpha为0.05
private double calcG(double alpha, int n) {
double[] N = { 1.1546847100299753, 1.4962499999999703,
1.763678479497787, 1.9728167175443088, 2.1391059896012203,
2.2743651271139984, 2.386809875078279, 2.4820832497170997,
2.564121252001767, 2.6357330437346365, 2.698971864039854,
2.755372404941574, 2.8061052912205966, 2.8520798130619083,
2.894013795424427, 2.932482154393285, 2.9679513293748547,
3.0008041587489247, 3.031358153993366, 3.0598791335206963,
3.086591582831163, 3.1116865231590722, 3.135327688211162,
3.157656337622164, 3.178795077984819, 3.198850919445483,
3.2179177419513314, 3.2360783011390764, 3.2534058719727748,
3.26996560491852, 3.2858156522011304, 3.301008108808857,
3.31558980320037, 3.329602965279218, 3.3430857935316243,
3.356072938839107, 3.368595919061223, 3.3806834758032323,
3.3923618826659503, 3.403655212591846, 3.41458557057518,
3.4251732969213213, 3.435437145364717, 3.4453944396432576,
3.4550612115453876, 3.464452322969104, 3.4735815741386,
3.482461799798589, 3.491104954935569, 3.4995221913492585,
3.507723926208097, 3.5157199035634887, 3.5235192496631433,
3.5311305227901078, 3.5385617582575746, 3.5458205091071684,
3.5529138829882037, 3.5598485756350797 };
return N[n - 3];
}
}