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;
}