Triangular Distribution in VBA - excel

Question

What I currently have:
Option Explicit
Function Triangular(a As Double, b As Double, c As Double) As Double
Randomize
Application.Volatile
Dim d As Double
Dim uniform As Double
Dim retval as Double
d = (b - a) / (c - a)
uniform = Rnd()
If uniform <= d Then
Triangular = a + (c - a) * Sqr(d * uniform)
Else
Triangular = a + (c - a) * (1 - Sqr(1 - d) * (1 - uniform))
End If
End Function
I'm having trouble in regards to creating a triangular distribution function in VBA, which calculates a random number from arguments made from:
Calculate d = ( b - a )/( c - a )
Generate a uniformly distributed random number U between 0 and 1 with VBA's Rnd function.
If U <= d, return a + ( c - a ) × sqr(d×U) as the random number. (Sqr(x) is a VBA function which returns the square root of x.
If U > d , return a + ( c - a ) × (1 - sqr((1- d )×(1-U))) as the random number.
The parameters a and c are the minimum and maximum possible values respectively, and
the parameter b is the most likely value (where you see the high point in the triangle).
I'm unsure on how to create this function and was wondering if someone could lend a hand? In working on the function I realize I need to use randomize function in order to not generate similar results each time the function is called, as well as the application.volatile operation.

Answer 1

You have a bug in the code. Should be in second branch
Triangular = a + (c - a) * (1 - Sqr((1 - d) * (1 - uniform)))

Answer 2

Not sure of the correctness of your generating equations. Take a look Here for the correct equations; with the difference that b and c are switched with respect to your definition. Here's an implementation adapting the formulas of that page to your own definitions of a, b and c:
Function Triangular(a As Double, b As Double, c As Double) As Double
Application.Volatile
Dim U As Double: U = Rnd()
If U < (b - a) / (c - a) Then
Triangular = a + sqrt(U * (b - a) * (c - a))
Else
Triangular = c - sqrt(U * (c - b) * (c - a))
End If
End Function
To generate a sequence from the above distribution in a new Worksheet, you can
1- Create the new worksheet
2- Write your parameters in cells A1, B1 and C1
3- write this formula in A2: =Triangular($A$1, $B$1, $C$1)
4- Copy/Paste cell A2 down the column

Answer 3

Please notice (1-Prob) in the second case. The Wikipedia link shows the correct formula but it was not implemented correctly by A.S.H.
Function Triangular(ByVal Min As Single, ByVal ML As Single, ByVal Max As Single) As Single
Application.Volatile
Dim Prob As Single
Prob = Rnd
If Prob < (ML - Min) / (Max - Min) Then
Triangular = Min + Sqr(Prob * (ML - Min) * (Max - Min))
Else
Triangular = Max - Sqr((1 - Prob) * (Max - ML) * (Max - Min))
End If
End Function