Try:
Sub main()
Dim i As Integer
Application.ScreenUpdating = False
For i = 1 To 100
Cells(i, "A") = random_Poisson(1.25)
Next i
End Sub

Public Function random_Poisson(Mean As Double) As Double
Dim e As Double, p As Double
e = Exp(-Mean)
p = 1
Do Until (p < e)
random_Poisson = random_Poisson + 1
p = p * Rnd()
Loop
random_Poisson = random_Poisson - 1
End Function