Option Explicit

Function StudT(t As Double, n As Double) As Double
Dim th As Double
Dim Pi As Double

    Pi = (4 * Atn(1)) / 2
    th = Atn(Abs(t) / Sqr(n))

If n = 1 Then
        StudT = 1 - th / Pi
ElseIf n Mod 2 = 1 Then
        StudT = 1 - (th + Sin(th) * Cos(th) * StatCom(Cos(th) ^ 2, 2, n - 3)) / Pi
Else
        StudT = 1 - Sin(th) * StatCom(Cos(th) ^ 2, 1, n - 3)
End If
End Function

Private Function StatCom(q As Double, i As Double, j As Double) As Double
Dim z As Double
Dim zz As Double
Dim k As Double

zz = 1
z = 1

    For k = i To j Step 2
        zz = zz * q * k / (k + 1)
        z = z + zz
    Next
StatCom = z
End Function

Function AStudT(p As Double, n As Double) As Double
Dim v As Double
Dim dv As Double
Dim t As Double

v = 0.5
dv = 0.5

    While dv > 1E-18
        t = 1 / v - 1
        dv = dv / 2
    
        If StudT(t, n) > p Then
                v = v - dv
        Else:   v = v + dv
        End If
    Wend
AStudT = t
End Function
 

Function Student(p As Double, f1 As Double) As Double

Dim p4 As Double
Dim x0 As Double
Dim t As Double
Dim sMsg As String

With WorksheetFunction
    p4 = p * .Pi()
    
    ' точные значения
    If (f1 = 1) Then
        Student = -Cos(p4) / Sin(p4)
        Exit Function
    End If
  
    If f1 = 2 Then
        Student = Sqr(1# / (2# * p * (1# - p)) - 2#) * Sgn(p - 0.5)
        Exit Function
    End If
    
    ' Модификация Гольдберга и Левина приближения Пизера
    If (f1 - 1) * (f1 - 2) <> 0# Then
        x0 = NorDev(p)
        t = 1# + (1# + x0 * x0) / (4# * f1)
        t = t + (3# + 16# * x0 * x0 + 5 * (x0 ^ 4#)) / (96# * f1 * f1)
        t = x0 * t
    End If
End With

    Student = t

Exit Function
End Function

Private Function NorDev(p As Double) As Double
'On Error GoTo ErrH
  
Dim sMsg As String
'Dim sTit As String
Dim q As Double
Dim X As Double
Dim r As Double
Dim nd As Double

Dim a(4) As Double
Dim b(5) As Double
Dim c(4) As Double
Dim d(3) As Double
  
  a(0) = 2.50662823881
  a(1) = -18.6150006252
  a(2) = 41.39119773531
  a(3) = -25.44106049637
  b(0) = 0
  b(1) = -8.4735109309
  b(2) = 23.08336743743
  b(3) = -21.06224101826
  b(4) = 3.13082909833
  c(0) = -2.78718931138
  c(1) = -2.29796479134
  c(2) = 4.85014127135
  c(3) = 2.32121276858
  d(0) = 0
  d(1) = 3.54388924762
  d(2) = 1.63706781897

  q = p - 0.5
  If (Abs(q) > 0.42) Then      '  хвосты распределения
    r = p
    If (q > 0) Then r = 1 - p
    If (r <= 0) Then '    защита от неправильного ввода
      sMsg = "Ошибка данных : P = " & Format(p, "0.000") _
           & " и не принадлежит интервалу [0...1]"
    Else  '   аппроксимация для хвостов распределения
      r = Sqr(-Log(r))
      X = (((c(3) * r + c(2)) * r + c(1)) * r + c(0))
      If (q < 0) Then X = -X
      nd = X / ((d(2) * r + d(1)) * r + 1)
    End If

  Else  ' аппроксимация для центральной части распределения
    r = q * q
    X = q * (((a(3) * r + a(2)) * r + a(1)) * r + a(0))
    nd = X / ((((b(4) * r + b(3)) * r + b(2)) * r + b(1)) * r + 1)
  End If
  
  NorDev = nd
Exit Function
End Function