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;
}