public static BigDecimal Corr(string[] NumberSeries1, string[] NumberSeries2)
{
//相关系数计算
BigDecimal Mean1 = 0;
BigDecimal Mean2 = 0;
BigDecimal Variance1 = 0;
BigDecimal Variance2 = 0;
BigDecimal cov = Covariance(NumberSeries1, ref Mean1, ref Variance1, NumberSeries2, ref Mean2, ref Variance2);
BigDecimal Rho = cov / (MathV.Sqrt((Variance1 * Variance2).ToString())).ToString();
//计算相关系数
return(Rho);
}
public static string HypothesisTesting(DataTable MainDT, string ColName,
string Statistics, string Operation, string Tail, double Significance, double NullHypothesis)
{
//假设检验
//Statistics为统计量，Operation为运算(>,<,=)
//Tail为单尾双尾，这里内容为双侧、左单侧、右单侧
//Significance为显著性水平
int ColNum = Tabulation.FindCol(MainDT, ColName);
string[] Numbers = Tabulation.ReadVector(MainDT, ColNum).ToArray();
StringBuilder Result = new StringBuilder();
Result.Append("假设检验: ");
Result.Append(Statistics);
Result.Append("\r\n");
Result.Append("显著性水平: ");
Result.Append(Significance.ToString());
Result.Append("\t");
Result.Append(Tail);
Result.Append("\r\n原假设: ");
Result.Append(Statistics);
Result.Append(" ");
Result.Append(Operation);
Result.Append(" ");
Result.Append(NullHypothesis.ToString());
Result.Append("\r\n备择假设: ");
Result.Append(Statistics);
Result.Append(" ");
if (Operation == "=")
{
Result.Append("<>");
}
else if (Operation == "<=")
{
Result.Append(">");
}
else
{
Result.Append("<");
}
Result.Append(" ");
Result.Append(NullHypothesis.ToString());
Result.Append("\r\n");
BigDecimal sum = 0;
BigDecimal mean = 0;
BigDecimal Variance = 0;
BigDecimal Sd = 0;
//Sd为标准差
int count = 0;
BigDecimal sum2 = 0;
//sum2用于计算数字的平方，方便计算方差
Double TempNum = 0;
BigDecimal BigTemp = 0;
//BigTemp用于记录BigDecimal类型的临时数据
double Threshold = 0;
//Threshold为临界值
double PValue = 0;
//Pvalue不用多解释了吧～
foreach (string Num in Numbers)
{
if (Double.TryParse(Num, out TempNum))
{
sum += TempNum;
sum2 += (BigDecimal)TempNum * (BigDecimal)TempNum;
count++;
}
}
//遍历了该列所有数字
if (Statistics == "均值")
{
if (count >= 30)
{
Result.Append(HTHeader_Ztest);
}
else
{
Result.Append(HTHeader_Ttest);
}
if (count <= 1)
{
return("样本数量过少，无法进行假设检验！\r\n");
}
else
{
//开始计算均值和方差
//方差要乘以调整系数
mean = sum / count;
Variance = (sum2 / count - mean * mean) * count / (count - 1);
Result.Append(StrManipulation.PadLeftX(StrManipulation.VariableNamePolish(ColName), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(count.ToString(), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(mean.ToString()), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(MathV.Sqrt(Variance.ToString()).ToString()), ' ', 12));
Result.Append("\t");
if (count >= 30)
{
//大样本
//z检验
Sd = MathV.Sqrt(Variance.ToString()).ToString();
BigTemp = (mean - NullHypothesis) / (Sd / Math.Sqrt(count));
//BigTemp此时的值为z检验统计量
//样本数count无需大数开方，用普通方法开方即可
if (Tail == "双侧")
{
Threshold = NORMSINV(1 - Significance / 2);
PValue = 2 * (1 - NORMDIST(Math.Abs(Convert.ToDouble(BigTemp.ToString()))));
}
else if (Tail == "左单侧")
{
Threshold = NORMSINV(Significance);
PValue = 1 - NORMDIST(Math.Abs(Convert.ToDouble(BigTemp.ToString())));
}
else if (Tail == "右单侧")
{
Threshold = NORMSINV(1 - Significance);
PValue = 1 - NORMDIST(Math.Abs(Convert.ToDouble(BigTemp.ToString())));
}
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(BigTemp.ToString()), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(Threshold.ToString()), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(PValue.ToString()), ' ', 12));
Result.Append("\r\n");
if (PValue < Significance)
{
Result.Append("在");
Result.Append(Significance.ToString());
Result.Append("的显著性水平上拒绝原假设");
}
else
{
Result.Append("在");
Result.Append(Significance.ToString());
Result.Append("的显著性水平上不拒绝原假设");
}
}
else
{
//小样本
//t检验
Sd = MathV.Sqrt(Variance.ToString()).ToString();
BigTemp = (mean - NullHypothesis) / (Sd / Math.Sqrt(count));
//BigTemp此时的值为z检验统计量
//样本数count无需大数开方，用普通方法开方即可
if (Tail == "双侧")
{
Threshold = TINV(Significance / 2 / 2, count - 1);
//每个放进TINV的值都要除以2，这个bug之后会进行修复
PValue = TDIST(Math.Abs(Convert.ToDouble(BigTemp.ToString()) / 2), count - 1, 2);
}
else if (Tail == "左单侧")
{
Threshold = TINV(Significance / 2, count - 1);
PValue = TDIST(Math.Abs(Convert.ToDouble(BigTemp.ToString()) / 2), count - 1, 1);
}
else if (Tail == "右单侧")
{
Threshold = TINV(Significance / 2, count - 1);
PValue = TDIST(Math.Abs(Convert.ToDouble(BigTemp.ToString()) / 2), count - 1, 1);
}
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(BigTemp.ToString()), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(Threshold.ToString()), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(PValue.ToString()), ' ', 12));
Result.Append("\r\n");
if (PValue < Significance)
{
Result.Append("在");
Result.Append(Significance.ToString());
Result.Append("的显著性水平上拒绝原假设");
}
else
{
Result.Append("在");
Result.Append(Significance.ToString());
Result.Append("的显著性水平上不拒绝原假设");
}
}
Result.Append("\r\n");
return(Result.ToString());
}
}
else if (Statistics == "比率")
{
return("hhh");
}
else
{
//方差
return("hhh");
}
}
public static string QuickSummary(DataTable MainDT, int ColNum)
{
string ColName = MainDT.Columns[ColNum].ColumnName;
List <string> Numbers = Tabulation.ReadVector(MainDT, ColNum);
StringBuilder Result = new StringBuilder();
BigDecimal sum = 0;
BigDecimal mean = 0;
BigDecimal Variance = 0;
int count = 0;
BigDecimal max = 0;
BigDecimal min = 0;
BigDecimal sum2 = 0;
Double TempNum = 0;
//sum2用于计算数字的平方，方便计算方差
foreach (string Num in Numbers)
{
if (Double.TryParse(Num, out TempNum))
{
sum += TempNum;
sum2 += (BigDecimal)TempNum * (BigDecimal)TempNum;
count++;
if (count == 1)
{
max = TempNum;
min = TempNum;
}
else
{
if (max < TempNum)
{
max = TempNum;
}
if (min > TempNum)
{
min = TempNum;
}
}
}
}
if (count == 0)
{
//如果没有获取任何数字
return("");
}
else if (count == 1)
{
//如果只有一个数字，可以计算均值，但是不可以计算标准差
mean = sum / count;
Result.Append(StrManipulation.PadLeftX(StrManipulation.VariableNamePolish(ColName), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(count.ToString(), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(mean.ToString()), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX("NA", ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(min.ToString()), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(max.ToString()), ' ', 12));
Result.Append("\r\n");
//Temp += Result;
return(Result.ToString());
}
else
{
//开始计算均值和方差
//方差要乘以调整系数
mean = sum / count;
Variance = (sum2 / count - mean * mean) * count / (count - 1);
Result.Append(StrManipulation.PadLeftX(StrManipulation.VariableNamePolish(ColName), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(count.ToString(), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(mean.ToString()), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(MathV.Sqrt(Variance.ToString()).ToString()), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(min.ToString()), ' ', 12));
Result.Append("\t");
Result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(max.ToString()), ' ', 12));
Result.Append("\r\n");
return(Result.ToString());
}
}
public static string CI(string VarName, string [] Numbers, string Tail, string Statistics, double Significance)
{
//Confidence Interval 置信区间
//Tail为单双尾,Tail = "单尾"，Tail = "双尾"
//Statistics为统计量 "均值" "比例"
int count = 0;
//count用于统计样本个数
StringBuilder result = new StringBuilder();
//result记录反馈结果
BigDecimal Sd = 0;
//Sd为标准差
double Temp = 0;
//Temp用于记录临时数据
BigDecimal BigTemp = 0;
//BigTemp用于记录BigDecimal类型的临时数据
if (Tail == "双尾")
{
Significance = 1 - (1 - Significance) / 2;
// 1 - (1 - 0.95)/2
}
if (Statistics == "均值" || Statistics == "方差")
{
BigDecimal Mean = 0;
BigDecimal Sum = 0;
BigDecimal Sum2 = 0;
foreach (string Num in Numbers)
{
if (double.TryParse(Num, out Temp))
{
Sum += Temp;
Sum2 += (BigDecimal)Temp * (BigDecimal)Temp;
count++;
}
}
if (count <= 1)
{
return("样本数量过少，无法进行参数估计");
}
else
{
Mean = Sum / count;
BigDecimal Variance = (Sum2 / count - Mean * Mean) * count / (count - 1);
Sd = MathV.Sqrt(Variance.ToString()).ToString();
result.Append(StrManipulation.PadLeftX(StrManipulation.VariableNamePolish(VarName), ' ', 12));
result.Append("\t");
result.Append(StrManipulation.PadLeftX(count.ToString(), ' ', 12));
result.Append("\t");
result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(Mean.ToString()), ' ', 12));
result.Append("\t");
result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(Sd.ToString()), ' ', 12));
result.Append("\t");
if (Statistics == "均值")
{
if (count >= 30)
{
//大样本
BigTemp = NORMSINV(Significance) * Sd / MathV.Sqrt(count).ToString();
}
else
{
//小样本
BigTemp = TINV(1 - Significance, (count - 1)) * Sd / MathV.Sqrt(count).ToString();
}
result.Append(StrManipulation.PadLeftX(MathV.NumberPolish((Mean - BigTemp).ToString()), ' ', 12));
result.Append("\t");
result.Append(StrManipulation.PadLeftX(MathV.NumberPolish((Mean + BigTemp).ToString()), ' ', 12));
result.Append("\r\n");
}
else
{
//Statistics == "方差"
BigTemp = (count - 1) * Variance;
result.Append(StrManipulation.PadLeftX(MathV.NumberPolish((BigTemp / Stat.chi2Ua(1 - Significance, count - 1)).ToString()), ' ', 12));
result.Append("\t");
MessageBox.Show(Significance.ToString());
MessageBox.Show(Stat.chi2Ua(Significance, count - 1).ToString());
result.Append(StrManipulation.PadLeftX(MathV.NumberPolish((BigTemp / Stat.chi2Ua(Significance, count - 1)).ToString()), ' ', 12));
result.Append("\r\n");
}
return(result.ToString());
}
}
else if (Statistics == "比例")
{
int OneCounts = 0;
int ZeroCounts = 0;
foreach (string Num in Numbers)
{
if (Num.Trim() == "1")
{
OneCounts++;
}
else if (Num.Trim() == "0")
{
ZeroCounts++;
}
}
if (ZeroCounts + OneCounts == 0)
{
return("样本不存在，无法进行参数估计\r\n");
}
else
{
if (ZeroCounts + OneCounts < 30)
{
result.Append("样本数量较少，进行比例的参数估计可能会不稳定\r\n");
}
BigDecimal Proportion = (BigDecimal)OneCounts / ((BigDecimal)ZeroCounts + (BigDecimal)OneCounts);
count = ZeroCounts + OneCounts;
result.Append(StrManipulation.PadLeftX(StrManipulation.VariableNamePolish(VarName), ' ', 12));
result.Append("\t");
result.Append(StrManipulation.PadLeftX((ZeroCounts + OneCounts).ToString(), ' ', 12));
result.Append("\t");
result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(Proportion.ToString()), ' ', 12));
result.Append("\t");
BigTemp = Proportion * (1 - Proportion);
result.Append(StrManipulation.PadLeftX(MathV.NumberPolish(MathV.Sqrt(BigTemp.ToString()).ToString()), ' ', 12));
result.Append("\t");
BigTemp = NORMSINV(Significance) * ((BigDecimal)MathV.Sqrt(BigTemp.ToString()).ToString() / (BigDecimal)MathV.Sqrt(count).ToString());
result.Append(StrManipulation.PadLeftX(MathV.NumberPolish((Proportion - BigTemp).ToString()).ToString(), ' ', 12));
result.Append("\t");
result.Append(StrManipulation.PadLeftX(MathV.NumberPolish((Proportion + BigTemp).ToString()).ToString(), ' ', 12));
result.Append("\r\n");
return(result.ToString());
}
}
else
{
return("未知统计量\r\n");
}
}
