您的位置: 首页 > IT文章 > 天文分析与计算——年均流量趋势检验(Mann-Kendall法、线性回归法) 天文分析与计算——年均流量趋势检验(Mann-Kendall法、线性回归法) 分类: IT文章 • 2022-07-25 00:00:06 水文分析与计算——年均流量趋势检验(Mann-Kendall法、线性回归法)//年均流量趋势检验.h //年均流量Mann-Kendall法趋势分析 void MannKendall() { using namespace std; int S = 0;//检验的统计变量 double VarS,//统计变量S的方差 Z ;//标准正态统计变量方差 S = 0; for(int i = 0; i < Y; i++) for(int j = i + 1; j < Y; j++) { if(YearQ[j]>YearQ[i]) S++; if(YearQ[j]<YearQ[i]) S--; } VarS = 0; VarS = Y*(Y - 1)*(2*Y + 5)/18.0; if(S > 0) Z = (S - 1)/pow(VarS, 0.5); if(S < 0) Z = (S + 1)/pow(VarS, 0.5); cout<<"年均流量趋势检验——Mann-Kendall检验："<<endl <<"标准正态统计变量Z= "<<Z<<endl <<"Mann-Kendall检验通过请输入1,否则请关闭！"<<endl; cin>>Z;//控制台停留 cout<<endl; } //年均流量线性回归法法趋势分析 double Normal(double z) {//返回标准正态分布的密度函数 double temp; temp=exp((-1)*z*z/2)/sqrt(2*PI); return temp; } double NormSDist(const double z) {//返回标准正态分布的累积频率函数 if(z > 6) return 1; if(z < -6) return 0; static const double gamma = 0.231641900, a1 = 0.319381530, a2 = -0.356563782, a3 = 1.781477973, a4 = -1.821255978, a5 = 1.330274429; double k = 1.0 / (1 + fabs(z) * gamma); double n = k * (a1 + k * (a2 + k * (a3 + k * (a4 + k * a5)))); n = 1 - Normal(z) * n; if(z < 0) return 1.0 - n; return n; } void XianXingJianYan() {//线性回归检验 using namespace std; double AverageYearQ = 0, AverageT = (1+Y)/2.0, a, b,//待定回归系数 r = 0,//线性相关系数 t,//t统计量 sigmaT =0, sigmaYearQ = 0,//均方差 NewYearQ[Y],//按升序排列的年均流量 Fn,//样本累积频率 F0,//理论累积频率 D_n_alpha = 0.202737,//显著水平为alpha且样本容量为n时的拒绝临界值 MaxD = 0,//max(|Fn - F0|) temp, sigmab = 0;//回归系数b标准方差 // int order;//升序排序年均流量 for(int i = 0; i < Y; i++) { AverageYearQ += YearQ[i]; } AverageYearQ /= Y; for(int i = 0; i < Y; i++) { r += (i - AverageT)*(YearQ[i] - AverageYearQ); sigmaT += pow(i - AverageT, 2); sigmaYearQ += pow(YearQ[i] - AverageYearQ, 2); } r /= pow(sigmaT*sigmaYearQ, 0.5); sigmaT = pow(sigmaT/(Y - 1), 0.5); sigmaYearQ = pow(sigmaYearQ/(Y - 1), 0.5); for(int i = 0; i < Y; i++) NewYearQ[i] = YearQ[i]; for(int i = 0; i < Y - 1; i++) { for(int j = i + 1; j < Y; j++) if(NewYearQ[i] > NewYearQ[j]) { temp = NewYearQ[i]; NewYearQ[i] = NewYearQ[j]; NewYearQ[j] = temp; } } for(int i = 0; i < Y; i++) { Fn = (double)(i+1)/(Y + 1); F0 = NormSDist((NewYearQ[i] - AverageYearQ)/sigmaYearQ); if(MaxD < fabs(Fn - F0)) MaxD = fabs(Fn - F0); } cout<<"年均流量趋势检验——线性回归检验："<<endl <<"正态分布K-S检验统计量D ="<<MaxD<<endl <<"K-S检验拒绝临界值D(n, a)="<<D_n_alpha<<endl; b = r*sigmaYearQ/sigmaT; a = AverageYearQ - b*AverageT; for(int i = 0; i < Y; i++) sigmab += pow(YearQ[i] - (a + b*i), 2); sigmab = pow(sigmab/(Y - 2), 0.5)/(pow(sigmaT, 2)*(Y - 1)); t = b/sigmab; cout<<"线性相关系数r = "<<r<<endl <<"年均流量Q倚时序t的回归系数估计值分别为："<<endl <<"a = "<<a<<endl <<"b = "<<b<<endl <<"假设检验统计量t = "<<t<<endl <<"线性回归检验通过请输入1,否则请关闭！"<<endl; cin>>t;//控制台停留 cout<<endl<<endl<<endl; }
