Excel 宏编程：Bootstrap 抽样与最小二乘法计算 Weibull 参数

由于题目中没有给出具体的数据和要求的 Weibull 参数，下面给出一个示例代码，以说明如何编写 Excel 宏来进行 Bootstrap 抽样和最小二乘法计算 Weibull 参数。

首先，我们假设我们需要计算一组数据的 Weibull 参数，并使用 Bootstrap 方法来估计参数的置信区间。我们将数据保存在 Excel 工作簿中，其中第一列为样本编号，第二列为观测值。我们可以编写以下代码来读取数据：

Sub Get_Data()
    Dim dataRange As Range
    Dim data() As Double
    Dim n As Long
    Dim i As Long
    
    ' Get data range
    Set dataRange = Application.InputBox(prompt:="Select data range", Type:=8)
    
    ' Get number of data points
    n = dataRange.Rows.Count - 1
    
    ' Resize data array
    ReDim data(1 To n)
    
    ' Populate data array
    For i = 1 To n
        data(i) = dataRange.Cells(i + 1, 2).Value
    Next i
    
    ' Call Weibull function to calculate parameters
    Call Weibull(data)
End Sub

接下来，我们可以编写一个 Weibull 函数来计算参数。我们可以使用最小二乘法来拟合 Weibull 分布，即找到最小化残差平方和的参数。在这个函数中，我们将使用 Excel 内置的 LSQNONLIN 函数来求解最小二乘问题。代码如下：

Function Weibull(data() As Double) As Double()
    Dim alpha As Double
    Dim beta As Double
    Dim rss As Double
    Dim params(1 To 2) As Double
    Dim xdata() As Double
    Dim ydata() As Double
    Dim i As Long
    
    ' Resize xdata and ydata arrays
    ReDim xdata(1 To UBound(data))
    ReDim ydata(1 To UBound(data))
    
    ' Sort data in ascending order
    Call QuickSort(data, 1, UBound(data))
    
    ' Populate xdata and ydata arrays
    For i = 1 To UBound(data)
        xdata(i) = Log(data(i))
        ydata(i) = Log(-Log(1 - i / (UBound(data) + 1)))
    Next i
    
    ' Use LSQNONLIN to minimize residual sum of squares
    params(1) = 1
    params(2) = 1
    Call Application.Run("LSQNONLIN", params, xdata, ydata)
    
    alpha = Exp(params(1))
    beta = Exp(-params(2) / params(1))
    
    ' Output results
    Debug.Print "Alpha: " & alpha
    Debug.Print "Beta: " & beta
    
    ' Return parameters
    ReDim Weibull(1 To 2)
    Weibull(1) = alpha
    Weibull(2) = beta
End Function

在计算 Weibull 参数之后，我们可以使用 Bootstrap 方法来估计参数的置信区间。我们可以编写以下代码来执行 Bootstrap 抽样并计算参数的置信区间：

Sub Bootstrap(data() As Double, nBoot As Long)
    Dim alpha() As Double
    Dim beta() As Double
    Dim n As Long
    Dim i As Long
    Dim j As Long
    Dim k As Long
    Dim sample() As Double
    Dim params() As Double
    Dim meanAlpha As Double
    Dim meanBeta As Double
    Dim stdAlpha As Double
    Dim stdBeta As Double
    
    ' Get number of data points
    n = UBound(data)
    
    ' Resize alpha and beta arrays
    ReDim alpha(1 To nBoot)
    ReDim beta(1 To nBoot)
    
    ' Perform bootstrap sampling
    For i = 1 To nBoot
        ' Resize sample array
        ReDim sample(1 To n)
        
        ' Generate random sample
        For j = 1 To n
            k = Int(Rnd() * n) + 1
            sample(j) = data(k)
        Next j
        
        ' Calculate Weibull parameters for sample
        params = Weibull(sample)
        
        ' Store parameters
        alpha(i) = params(1)
        beta(i) = params(2)
    Next i
    
    ' Calculate mean and standard deviation of parameters
    meanAlpha = Application.WorksheetFunction.Average(alpha)
    meanBeta = Application.WorksheetFunction.Average(beta)
    stdAlpha = Application.WorksheetFunction.StDev(alpha)
    stdBeta = Application.WorksheetFunction.StDev(beta)
    
    ' Output results
    Debug.Print "Alpha Mean: " & meanAlpha
    Debug.Print "Alpha Std: " & stdAlpha
    Debug.Print "Beta Mean: " & meanBeta
    Debug.Print "Beta Std: " & stdBeta
End Sub

最后，我们可以调用 Bootstrap 函数来执行 Bootstrap 抽样并输出结果。例如，我们可以使用以下代码来执行 1000 次 Bootstrap 抽样：

Sub Run_Bootstrap()
    Dim dataRange As Range
    Dim data() As Double
    Dim nBoot As Long
    
    ' Get data range
    Set dataRange = Application.InputBox(prompt:="Select data range", Type:=8)
    
    ' Get number of bootstrap samples
    nBoot = 1000
    
    ' Get data
    data = dataRange.Columns(2).Value
    
    ' Call Bootstrap function
    Call Bootstrap(data, nBoot)
End Sub

注意，这只是一个示例代码，具体实现可能需要根据具体情况进行调整。