Hydrological Analysis and Calculation-average annual traffic trend test (Mann-Kendall method and linear regression method)

[Cpp]
// Average annual traffic trend test. h
 
// Trend analysis of average annual traffic using the Mann-Kendall Method
Void MannKendall ()
{
Using namespace std;
Int S = 0; // The Statistical variable for the test
Double VarS, // returns the variance of variable S.
Z; // standard normal statistical variable variance
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 <"average annual traffic trend test -- Mann-Kendall test:" <endl
<"Standard normal statistical variable Z =" <Z <endl
<"Input 1 if the Mann-Kendall test is passed; otherwise, disable it! "<Endl;
Cin> Z; // stay on the console
Cout <endl;
}
 
 
// Trend Analysis Based on Linear Regression of average annual traffic
Double Normal (double z)
{// Returns the density function of the standard normal distribution.
Double temp;
Temp = exp (-1) * z/2)/sqrt (2 * PI );
Return temp;
}
Double NormSDist (const double z)
{// Returns the cumulative frequency function of the standard normal distribution.
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 ()
{// Linear regression test
Using namespace std;
Double AverageYearQ = 0,
AverageT = (1 + Y)/2.0,
A, B, // undetermined Regression Coefficient
R = 0, // linear correlation coefficient
T, // t statistic
SigmaT = 0,
SigmaYearQ = 0, // Mean Deviation
NewYearQ [Y], // average annual traffic in ascending order
Fn, // sample accumulation frequency
F0, // theoretical accumulation frequency
D_n_alpha = 0.202737, // rejection threshold when the notable level is alpha and the sample size is n
MaxD = 0, // max (| Fn-F0 |)
Temp,
Sigmonoclonal = 0; // regression coefficient B standard variance
// Int order; // average annual traffic in ascending order
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 <"average annual traffic trend test-linear regression test:" <endl
<"Normal Distribution K-S test statistic D =" <MaxD <endl
<"Critical Rejection Value of K-S test D (n, a) =" <D_n_alpha <endl;
B = r * sigmaYearQ/sigmaT;
A = AverageYearQ-B * AverageT;
For (int I = 0; I <Y; I ++)
Sigmonoclonal + = pow (YearQ [I]-(a + B * I), 2 );
Sigmonoclonal = pow (sigmonoclonal/(Y-2), 0.5)/(pow (sigmaT, 2) * (Y-1 ));
T = B/sigmonoclonal;
Cout <"linear correlation coefficient r =" <r <endl
<"The regression coefficient of the Q-dependent time series t of the average annual traffic is:" <endl
<"A =" <a <endl
<"B =" <B <endl
<"Hypothesis test statistic t =" <t <endl
<"Enter 1 if the linear regression test is passed; otherwise, disable it! "<Endl;
Cin> t; // stay on the console
Cout <endl;
}
By: Superwen_go