EXCEL 2016 PDF course outline


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Formation Excel en ligne par vidéo

205 leçons vidéos + 20 Livres PDF + 20 TP + Sous supervision + Certificat de réussite à la fin du cours



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Excel VBA Basic Tutorial 1

This page contains the 1st lesson on the Excel VBA Basic Tutorial series.  It covers topics in creating and managing array and understanding the VBA decision and loop structures.  Beginners in VBA programming are encouraged to go through the prior lessons in this series if they had not already done so.  This document contains information about the following topics.

•   

•   

•   

Creating Your First Macro 

In this sub section, we will show you how to create your first macro (VBA program).   We will use the world classic "Hello World!" example.  To create the example, please follow the following steps:

1.   Open Visual Basic Editor by go to Tools Macro Visual Basic Editor or just simply press the [Alt] and [F11] keys at the same time.

 

2.   In the Insert menu on top of the Visual Basic Editor, select Module to open the Module window (code window).

3.   In the Module window, type the following:

Sub showMessage()

MsgBox "Hello World!"

End Sub

 

4.   Click the Run  button,, press [F5], or go to Run..Run Sub/UserForm to run the program

 

5.   The message box pops up with the "Hello World!" greeting.

 

Macrosoft Excel has a build-in macro recorder that translates your actions into VBA macro commands.  After you recorded the macro, you will be able to see the layout and syntax.  Before you record or write a macro, plan the steps and commands you want the macro to perform.  Every actions that you take during the recording of the macro will be recorded - including the correction that you made.

In this example, we will record a macro that sets the cell background color to light yellow.  To

3.       In the Background Color Panel, select the Ligth Yellow color box.  This action will set the background of the current cell (A1) in light yellow color.

4.       To stop the macro recording, click the Stop button (the navy blue rectangle) on the Macro Recorder toolbar.

 

See the Recorded Syntax

The recorded macro is ready for use.  Before we run the marco, let's look into the syntax.

1.   To load the Visual Basic Editor, press [Alt] and [F11] at the same time.  (Remember from our prior lesson?)  The Visual Basic Editor comes up.

 

2.   Expand the Modules folder in the Project Explorer by clicking on the plus (+) sign.

 

3.   Double click the Module1 folder to see the sub routine (marco).

 

As the figure shows, the name of the sub routine is "SetBackgroundColor".   The color index for the light yellow is 36.  The background pattern is soild.

 

Run the Recorded Macro

In our prior example, we created the "Hello World!" marco.  We ran the macro within the Visual Basic Editor.  This time we will run the recorded macro in the worksheet.

1.  On any worksheet, select from D3 to E6.

 

4.   Cells D3 to E6 now have light yellow background color.

 

Modules and Procedures

Modules and Procedures and Their Scope

A module is a container for procedures as shown in our prior examples.  A procedure is a unit of code enclosed either between the Sub and End Sub statement or between the Function and End Function statements.  

The following sub procedure (or sub routine) print the current date and time on cell C1:

Sub ShowTime()

Range("C1") = Now() End Sub

The following function sum up two numbers:

Function sumNo(x, y)      sumNo = x + y End Function

Procedures in Visual Basic can have either private or public scope.  A procedure with private scope is only accessible to the other procedures in the same module; a procedure with public scope is accessible to all procedures in in every module in the workbook in which the procedure is declared, and in all workbooks that contain a reference to that workbook.  By default, procedures has public scope.

Here are examples of defining the scope for procedure. 

Public Sub ShowTime()

Range("C1") = Now() End Sub

Private Sub ShowTime()

Range("C1") = Now()

End Sub

 

Calling Sub Procedures and Function Procedures

There are two ways to call a sub procedure.  The following example shows how a sub procedure can be called by other sub procedures. 

Sub z(a)

MsgBox a End Sub

Sub x()

    Call z("ABC")

End Sub

Sub y()     z "ABC" End Sub

Sub z procedure takes an argument (a) and display the argument value ("ABC") in a message box.  Running either Sub x or Sub y will yield the same result.

The following example calls a function procedure from a sub procedure.

Sub ShowSum()      msgbox sumNo(3,5) End Sub

Function sumNo(x, y)      sumNo = x + y End Function

The ShowSum sub procedure calls the sumNo function and returns an "8" in a message box.

If there are procedures with duplicate names in different modules, you must need to include a module qualifier before the procedure name when calling the procedure. 

For example:

Module1.ShowSum

 

Passing Argument by Reference or by Value

If you pass an argument by reference when calling a procedure, the procedure access to the actual variable in memory.  As a result, the variable's value can be changed by the procedure.  Passing by reference is the default in VBA.  If you do not explicitly specify to pass an argurment by value, VBA will pass it by reference.  The following two statements yield the same outcome. 

Sub AddNo(ByRef x as integer)

Sub AddNo(x as integer)

Here is an example to show the by reference behavior.  The sub procedure, TestPassing 1 calls AddNo1 by reference and display "60" (50 + 10) on the message box.

Sub TestPassing1()     Dim y As Integer     y = 50     AddNo1 y

MsgBox y

End Sub

Sub AddNo1(ByRef x As Integer)     x = x + 10 End Sub

The following example shows the by value behavior.  The sub procedure, TestPassing 2 calls AddNo2 by value and display "50" on the message box.

Sub TestPassing2()     Dim y As Integer     y = 50     AddNo2 y

MsgBox y

End Sub

Sub AddNo2(ByVal x As Integer)     x = x + 10 End Sub

 

Excel VBA Basic Tutorial 2

This page contains the 2nd lesson on the Excel VBA Basic Tutorial series.  It covers topics in the most used Excel objects and collections.  Beginners in VBA programming are encouraged to go through the 1st lessons in this series if they had not already done so.  This document contains information about the following topics.

Objects and Collections

Workbook and Worksheet Object

Range Object and Cells Property

Methods and Property

Assigning Object Variables and Using Named Argument

Microsoft Support site or the Excel VBA Help section on your computer contains comprehensive examples on most the issues covered on this page.  For more information, please refer to them.

 

Objects and Collections   Microsoft Support

Objects are the fundamental building blocks of Visual Basic.  An object is a special type of variable that contains both data and codes.  A collection is a group of objects of the same class.  The most used Excel objects in VBA programming are Workbook, Worksheet, Sheet, and Range.

Workbooks is a collection of all Workbook objects.  Worksheets is a collection of Worksheet objects.

The Workbook object represents a workbook, the Worksheet object represents a worksheet, the Sheet object represents a worksheet or chartsheet, and the Range object represents a range of cells.

The following figure shows all the objects mentioned.  The workbook (Excel file) is currently .  The current worksheet is Sheet1 as the Sheet Tab indicated.  Two ranges are selected, range B2 and B7:B11.

 

Workbook and Worksheet Object

A workbook is the same as an Excel file.  The Workbook collection contains all the workbooks that are currently opened. Inside of a workbook contains at least one worksheet.   In VBA, a worksheet can be referenced as followed:

Worksheets("Sheet1")

Worksheets("Sheet1") is the worksheet that named "Sheet1."

Another way to refer to a worksheet is to use number index like the following:

Worksheets(1)

The above refers to the first worksheet in the collection.

*  Note that Worksheets(1) is not necessary the same sheet as Worksheets("Sheet1").

Sheets is a collection of worksheets and chart sheets (if present).  A sheet can be indexed just like a worksheet.  Sheets(1) is the first sheet in the workbook.

To refer sheets (or other objects) with the same name, you have to qualify the object.  For example:

Workbooks("Book1").Worksheets("Sheet1")

Workbooks("Book2").Worksheets("Sheet1")

If the object is not qualified, the active or the current object (for example workbook or worksheet) is used.

The sheet tab on the buttom the spreadsheet (worksheet) shows which sheet is active.  As the figure below shows, the active sheet is "Sheet1" (show in bold font and white background).

 

*  You can change the color of the sheet tabs by right click the tab, choose Tab Color, then select the color for the tab.

The sub routine below shows the name of each sheet in the current opened workbook.  You can use For Each Next loop to loop throgh the Worksheets collection. 

Sub ShowWorkSheets()

    Dim mySheet As Worksheet

    For Each mySheet In Worksheets

MsgBox

    Next mySheet

End Sub

 

Range Object and Cells Property

Range represents a cell, a row, a column, a selection of cells containing one or more contiguous blocks of cells, or a 3-D range.  We will show you some examples on how Range object can be used.

The following example places text "AB" in range A1:B5, on Sheet2.

Worksheets("Sheet2").Range("A1:B5") = "AB"

:

Note that, Worksheets.Range("A1", "B5") = "AB" will yield the same result as the above example.

The following place "AAA" on cell A1, A3, and A5 on Sheet2.

Worksheets("Sheet2").Range("A1, A3, A5") = "AAA"

 

Range object has a Cells property.  This property is used in every VBA projects on this website (very important).  The Cells property takes one or two indexes as its parameters. 

For example,

Cells(index) or Cells(row, column)

where row is the row index and column is the column index. The following three statements are interchangable:

ActiveSheet.Range.Cells(1,1)

Range.Cells(1,1) Cells(1,1)

The following returns the same outcome:

Range("A1") = 123    and    Cells(1,1) = 123

The following puts "XYZ" on Cells(1,12) or Range("L1") assume cell A1 is the current cell:

Cells(12) = "XYZ"

The following puts "XYZ" on cell C3:

Range("B1:F5").cells(12) = "ZYZ"

 

* The small gray number on each of the cells is just for reference purpose only. They are used to show how the cells are indexed within the range.

Here is a sub routine that prints the corresponding row and column index from A1 to E5.

Sub CellsExample()

   For i = 1 To 5

For j = 1 To 5

Cells(i, j) = "Row " & i & "   Col " & j

Next j

   Next i

End Sub

 

Range object has an Offset property that can be very handy when one wants to move the active cell around.  The following examples demostrate how the Offset property can be implemented (assume the current cell before the move is E5):

ActiveCell.Offset(1,0) = 1                       Place a "1" one row under E5 (on E6)

 

ActiveCell.Offset(0,1) = 1                       Place a "1" one column to the right of E5 (on F5)

 

ActiveCell.Offset(0,-3) = 1                      Place a "1" three columns to the left of E5 (on B5)

   

Methods and Properties

Each object contains its own methods and properties.

A Property represents a built-in or user-defined characteristic of the object.  A method is an action that you perform with an object.  Below are examples of a method and a property for the Workbook Object:

Workbooks.Close

Close method close the active workbook

Workbooks.Count

Count property returns the number of workbooks that are currently opened

Some objects have default properties. For example, Range's default property is Value. The following yields the same outcome. 

Range("A1") = 1    and     Range("A1").Value = 1

Here are examples on how to set and to get a Range property value:

The following sets the value of range A1 or Cells(1,1)  as "2005".  It actually prints "2005" on A1.

Range("A1").Value = 2005

The following gets the value from range A1 or Cells(1,1).

X = Range("A1").Value

Method can be used with or without argument(s).  The following two examples demostrate this behavior.

Methods That Take No Arguments:

Worksheets("Sheet").Column("A:B").AutoFit

Methods That Take Arguments:

Worksheets("Sheet1").Range("A1:A10").Sort _

Worksheets("Sheet1").Range("A1")

Worksheets("Sheet1").Range("A1") is the Key (or column) to sort by.

 

Assigning Object Variables and Using Named Argument

Sometime a method takes more than one argument.  For example, the Open method for the Workbook

object, takes 12 arguments.  To open a workbook with password protection, you would need to write the following code:

"", , , ,"pswd"

Since this method takes so many arguments, it is easy to misplace the password argument.  To overcome this potential problem, one can use named arguments like the following example:

fileName:="", password:="pswd"

You can also assign an object to an object variable using the Set Statement.

For example:

Dim myRange as Range

Set myRange = Range("A1:A10")

 

Excel VBA Basic Tutorial 3

This page contains the 3rd lesson on the Excel VBA Basic Tutorial series.  It covers topics in creating and managing array and understanding the VBA decision and loop structures.  Beginners in VBA programming are encouraged to go through the prior lessons in this series if they had not already done so.  This document contains information about the following topics.

•   

Declare an Array With Dim Statement

Resize an Array With Redim Statement

Manage Dynamic Array

Create Multi-Dimensional Array

Find The Size of an Array

•   

•   

Microsoft Support site or the Excel VBA Help section on your computer contains comprehensive examples on most the issues covered on this page.  For more information, please refer to them.

 

Creating and Managing Array  

Declaring an Array With Dim Statement

An array is a set of sequentially indexed elements having the same intrinsic data type. Each element of an array has a unique identifying index number. Changes made to one element of an array don't affect the other elements. 

Before signing values to an array, the array needs to be created.  You can declare the array by using the Dim statement.

For example, to declare a one-dimensional array with 5 elements, type the following:

            Dim Arr(4)

The element’s index of the array starts from 0 unless Option Base 1 is specified in the public area (area outside of the sub procedure).  If Option Base 1 is specified, the index will start from 1.

The following example assigns values to the array and displays all values in a message box :

         Option Base 1

Sub assignArray( )                   Dim Arr(5)

                  Arr(1) = “Jan”

                  Arr(2) = “Feb”

                       Arr(3) = “Mar”

                       Arr(4) = “Apr”

                  Arr(5) = “May”

                  Msgbox Arr(1) & "-" & Arr(2) & "-" & Arr(3) & "-" & Arr(4) & "-" & Arr(5)

            End Sub       

* The number inside the array, i.e. Arr(1), is the index. One (1) is the index of the first element in the   array.

 

Resize an Array With Redim Statement

The ReDim statement is used to size or resize a dynamic array that has already been formally declared.

For example, if you have already declared an array with an element value of 5 and decided to change the number of the element to 6, you can do the following to resize the array:

            Redim Arr(6)

We incorporate it into our last example:

         Option Base 1

         Sub assignArray( )

                  'Dim Arr(5)

                  Redim Arr(6)

                  Arr(1) = “Jan”

                  Arr(2) = “Feb”

                  Arr(3) = “Mar”

                  Arr(4) = “Apr”

                  Arr(5) = “May”

                  Arr(6) = “Jun”

                  Msgbox Arr(1) & "-" & Arr(2) & "-" & Arr(3) & "-" & Arr(4) & "-" & Arr(5)             End Sub

Note that the Dim Arr(5) statement is commoned out, because leaving this original statement in the sub will causing a compile error.

 

Manage Dynamic Array

A word of caution in using the Redim Statement to resize an array - resize the array can erase the elements in it.  In the following example, all the values assigned prior to resize the array are erased.  Only the value assigned to the array after resize remains.

         Option Base 1

            Sub assignArray( )                 

                  Redim Arr(5)

                  Arr(1) = “Jan”

                  Arr(2) = “Feb”

                  Arr(3) = “Mar”

                  Arr(4) = “Apr”

                  Arr(5) = “May”

                  Redim Arr(6)

                  Arr(6) = “Jun”

                  Msgbox Arr(1) & "-" & Arr(2) & "-" & Arr(3) & "-" & Arr(4) & "-" & Arr(5) & "-" & Arr(6)

            End Sub

By replace the Redim Arr(6) with Redim Preserve Arr(6), all values will remain.  For example:

          Option Base 1

          Sub assignArray( )

                  Redim Arr(5)

           Arr(1) = “Jan”

                  Arr(2) = “Feb”

                  Arr(3) = “Mar”

                  Arr(4) = “Apr”

                  Arr(5) = “May”

                  Redim Preserve Arr(6)

                  Arr(6) = “Jun”

                  Msgbox Arr(1) & "-" & Arr(2) & "-" & Arr(3) & "-" & Arr(4) & "-" & Arr(5) & "-" & Arr(6)

            End Sub

 

Create Multi-Dimensional Array

An array can also store multiple dimensional data.  To simplify our tutorial, example on a twodimensional array is used.  Assume you have data of a local store's yearly sale in the following table and you want to store the data in a two-dimensional array:

                              Year 2003      Year 2004

           CD Sale            1,000           1,500          DVD Sale           1,200            2,000

First we create the array as follow:

Dim Arr(2,2)

Then we assign the values into the array.  We treat the first dimension as the year and the second dimension as the product sale:

            arr(1,1) = 1000             arr(1,2) = 1200             arr(2,1) = 1500 arr(2,2) = 2000

We now display the values of the array with a message box:

          Msgbox "Sale of CD in 2003 is " & arr(1,1) & vbCrLf  & "Sale of CD in 2004 is " _

& arr(2,1)  & vbCrLf  & "Sale of DVD in 2003 is " & arr(1,2) & vbCrLf _                         & "Sale of DVD in 2004 is " & arr(2,2) The complete procedure is as followed:

               Option Base 1

            Sub multDimArray( )            

                  Dim Arr(2,2)

           arr(1,1) = 1000                   arr(1,2) = 1200                   arr(2,1) = 1500                   arr(2,2) = 2000

                       Msgbox "Sale of CD in 2003 is " & arr(1,1) & vbCrLf  & "Sale of CD in 2004 is " _

                                   & arr(2,1) & vbCrLf  & "Sale of DVD in 2003 is " & arr(1,2) & vbCrLf  _                                    & "Sale of DVD in 2004 is " & arr(2,2)             End Sub

* vbCrLf stands for VB Carriage Return Line Feed.  It puts a return and a new line as shown in the   message box above.  The underscore "_" on the back of the first line of the message box means   "continue to the next line"

 

Find The Size of an Array

The largest available subscript for the indicated dimension of an array can be obtained by using the Ubound function. In our one-dimensional array example, Ubound(arr) is 5.

In our two-dimensional array example above, there are two upper bound figures - both are 2.  UBound returns the following values for an array with these dimensions*:

         Dim A(1 To 100, 0 To 3, -3 To 4)

          Statement Return Value  

         UBound(A, 1)                         100                  

         UBound(A, 2) 3

         UBound(A, 3)                            4

* Example taken from Excel VBA Help section.

The UBound function is used with the LBound function to determine the size of an array. Use the LBound function to find the lower limit of an array dimension.

          Statement Return Value  

         LBound(A, 1)                            1                  

         LBound(A, 2)                            0

         LBound(A, 3)                           -3

To get the size of an array, use the following formula:

        UBound(Arr) - LBound(Arr) + 1

For example:

 Ubound(A,1) - LBound(A,1) + 1

        = 100 - 1 + 1

        = 100

        Ubound(A,2) - LBound(A,2) + 1

        = 3 - 0 + 1



        = 4

        Ubound(A,3) - LBound(A,3) + 1

        = 4 - (-3) + 1

        = 8

For more information on arrays checkMicrosoft Support

 

Decision Structures - IF and Select Case

IF Then Statement

The IF Then is a single condition and run a single statement or a block of statement.

Example, the following statement set variable Status to "Adult" if the statement is true:

        If Age >= 18 Then Status = "Adult"

You can also use multiple-line block in the If statement as followed:

        If Ago >= 18 Then

            Status = "Adult"

            Vote = "Yes"

        End If

Note that in the multiple-line block case, End If statement is needed, where the single-line case does not.

 

IF Then Else

The If Then Else statement is used to define two blocks of conditions - true and false.

Example:

     If Age >=22 Then

        Drink = "Yes"

    Else

        Drink = "No"

    End If

Again, note that End If statement is needed in this case as well since there is more than one block of statements.

 

IF Then ElseIf

The IF Then ElseIf is used to test additional conditions without using new If Then statements.

For Example:

   If Age >= 18 and Age < 22 Then

        Msgbox "You can vote"

    ElseIf Age >=22 and Age < 62 Then

        Msgbox "You can drink and vote"

    ElseIf Age >=62 Then

        Msgbox "You are eligible to apply for Social Security Benefit"     Else

        Msgbox "You cannot drink or vote"     End If

Note that the last condition under Else is, implicitly, Age < 18.

 

Select Case

Select Case statement is an alternative to the ElseIf statement.  This method is more efficient and readable in coding the the If Then ElseIf statment. 

Example:

    Select Case Grade         Case Is >= 90

            LetterGrade = "A"         Case Is >= 80

            LetterGrade = "B"         Case Is >= 70

            LetterGrade = "C"

        Case Is >= 60

            LetterGrade = "D"

        Case Else

            LetterGrade = "Sorry"

    End Select

 

Loop Structures

For Next

Use For Next loop if the number of loops is already defined and known.  A For Next loop uses a counter variable that increases or decreases in value during each iteration of the loop.  This loop structure is being used the most for our examples on this site. 

Here is an example of the For Next loop:

    For i = 1 to 10

        Cells(i, 1) = i

    Next i

In this example, i is the counter variable from 1 to 10. The looping process will send value to the first column of the active sheet and print i (which is 1 to 10) to row 1 to 10 of that column.

Note that the counter variable, by default, increases by an increment of 1.

 

For Next Loop With Step

You can use the Step Keyword to sepcify a different increment for the counter variable. 

For example:

For i = 1 to 10 Step 2

        Cells(i, 1) = i     Next i

This looping process will print values with an increment of 2 on row 1, 3, 5, 7 and 9 on column one.

You can also have decrement in the loop by assign a negative value afte the Step keyword. 

For example:

    For i = 10 to 1 Step -2

        Cells(i, 1) = i

    Next i

This looping process will print values with an increment of -2 starts from 10 on row  10, 8, 6, 4 and 2 on column one.

 

Do While Loop

You can use the Do While Loop to test a condition at the start of the loop.  It will run the loop as long as the condition is ture and stops when the condition becomes false.  For Example:

   i = 1

    Do While i =< 10

        Cells(i, 1) = i         i = i + 1     Loop

This looping process yields the same result as in the For Next structures example.

One thing to be caution is that sometimes the loop might be a infinite loop.  And it happens when the condition never becomes false.  In such case, you can stop the loop by press [ESC] or [CTRL] + [BREAK].

 

Do Until Loop

You can test the condition at the beginning of the loop and then run the loop until the test condition becomes true.

Example:

    i = 1

    Do Until i = 11         Cells(i, 1) = i

        i = i + 1        Loop

This looping process yields the same result as in the For Next structures example.

 

Do Loop While

When you want to make sure that the loop will run at least once, you can put the test at the end of loop.  The loop will stop when the condition becomes false.   (compare this loop structure to the Do While Loop.)

For Example:

   i = 1     Do         Cells(i, 1) = i         i  = i + 1

    Loop While i < 11

This looping process yields the same result as in the For Next structures example.   

 

Do Loop Until

This loop structure, like the Do Loop While, makes sure that the loop will run at least once, you can put the test at the end of loop.  The loop will stop when the condition becomes true.   (compare this loop structure to the Do Until Loop.)

For Example:

   i = 1

    Do

        Cells(i, 1) = i         i  = i + 1

    Loop Until i = 11

This looping process yields the same result as in the For Next structures example.   

 

Excel VBA Simulation Basic Tutorial 101

This page contains basic Excel VBA skills needed for creating simulations.  Beginners who wish to learn simulation programming using Excel VBA are encouraged to go through the entire document if he or she had not already done so.  This tutorial is the prerequisite of Excel VBA SimulationBased Tutorial 201.  This document contains information about the following topics.

•   

Declare an Array With Dim Statement

Resize an Array With Redim Statement

Manage Dynamic Array

Create Multi-Dimensional Array

Find The Size of an Array

•   

•   

•   

•   

•   

Microsoft Support site or the Excel VBA Help section on your computer contains comprehensive examples on most the issues covered on this page.  For more information, please refer to them.

 

Creating and Managing Array  

Declaring an Array With Dim Statement

An array is a set of sequentially indexed elements having the same intrinsic data type. Each element of an array has a unique identifying index number. Changes made to one element of an array don't affect the other elements. 

Before signing values to an array, the array needs to be created.  You can declare the array by using the Dim statement.

For example, to declare a one-dimensional array with 5 elements, type the following:

            Dim Arr(4)

The element’s index of the array starts from 0 unless Option Base 1 is specified in the public area (area outside of the sub procedure).  If Option Base 1 is specified, the index will start from 1.

The following example assigns values to the array and displays all values in a message box :

         Option Base 1

Sub assignArray( )                   Dim Arr(5)

                  Arr(5) = “Jan”

                  Arr(2) = “Feb”

                       Arr(3) = “Mar”

                       Arr(4) = “Apr”

                  Arr(5) = “May”

                  Msgbox Arr(1) & "-" & Arr(2) & "-" & Arr(3) & "-" & Arr(4) & "-" & Arr(5)

            End Sub

* The number inside the array, i.e. Arr(1), is the index. One (1) is the index of the first element in the   array.

 

Resize an Array With Redim Statement

The ReDim statement is used to size or resize a dynamic array that has already been formally declared.

For example, if you have already declared an array with an element value of 5 and decided to change the number of the element to 6, you can do the following to resize the array:

            Redim Arr(6)

We incorporate it into our last example:

         Option Base 1

         Sub assignArray( )

                  'Dim Arr(5)

                  Redim Arr(6)

                  Arr(1) = “Jan”

                  Arr(2) = “Feb”

                  Arr(3) = “Mar”

                  Arr(4) = “Apr”

                  Arr(5) = “May”

                  Arr(6) = “Jun”

                  Msgbox Arr(1) & "-" & Arr(2) & "-" & Arr(3) & "-" & Arr(4) & "-" & Arr(5)             End Sub

Note that the Dim Arr(5) statement is commoned out, because leaving this original statement in the sub will causing a compile error.

 

Manage Dynamic Array

A word of caution in using the Redim Statement to resize an array - resize the array can erase the elements in it.  In the following example, all the values assigned prior to resize the array are erased.  Only the value assigned to the array after resize remains.

         Option Base 1

            Sub assignArray( )                 

                  Redim Arr(5)

                  Arr(1) = “Jan”

                  Arr(2) = “Feb”

                  Arr(3) = “Mar”

                  Arr(4) = “Apr”

                  Arr(5) = “May”

                  Redim Arr(6)

                  Arr(6) = “Jun”

                  Msgbox Arr(1) & "-" & Arr(2) & "-" & Arr(3) & "-" & Arr(4) & "-" & Arr(5) & "-" & Arr(6)

            End Sub

 

  By replace the Redim Arr(6) with Redim Preserve Arr(6), all values will remain.  For example:

          Option Base 1

          Sub assignArray( )                   Redim Arr(5)

                  Arr(1) = “Jan”

                  Arr(2) = “Feb”

                  Arr(3) = “Mar”

                  Arr(4) = “Apr”

                  Arr(5) = “May”

                  Redim Preserve Arr(6)

                  Arr(6) = “Jun”

                  Msgbox Arr(1) & "-" & Arr(2) & "-" & Arr(3) & "-" & Arr(4) & "-" & Arr(5) & "-" & Arr(6)

            End Sub

 

Create Multi-Dimensional Array

An array can also store multiple dimensional data.  To simplify our tutorial, example on a twodimensional array is used.  Assume you have data of a local store's yearly sale in the following table and you want to store the data in a two-dimensional array:

                              Year 2003      Year 2004

           CD Sale            1,000           1,500          DVD Sale           1,200            2,000

First we create the array as follow:

Dim Arr(2,2)

Then we assign the values into the array.  We treat the first dimension as the year and the second dimension as the product sale:

            arr(1,1) = 1000             arr(1,2) = 1200             arr(2,1) = 1500 arr(2,2) = 2000

We now display the values of the array with a message box:

          Msgbox "Sale of CD in 2003 is " & arr(1,1) & vbCrLf  & "Sale of CD in 2004 is " _

                                & arr(2,1) & vbCrLf  & "Sale of DVD in 2003 is " & arr(1,2) & vbCrLf  _ & "Sale of DVD in 2004 is " & arr(2,2)

The complete precedure is as followed:

         Option Base 1

            Sub multDimArray( )            

                  Dim Arr(2,2)

                  arr(1,1) = 1000 arr(1,2) = 1200                   arr(2,1) = 1500                   arr(2,2) = 2000

                       Msgbox "Sale of CD in 2003 is " & arr(1,1) & vbCrLf  & "Sale of CD in 2004 is " _

                                   & arr(2,1) & vbCrLf  & "Sale of DVD in 2003 is " & arr(1,2) & vbCrLf  _                                    & "Sale of DVD in 2004 is " & arr(2,2)             End Sub

* vbCrLf stands for VB Carriage Return Line Feed.  It puts a return and a new line as shown in the   message box above.  The underscore "_" on the back of the first line of the message box means   "continue to the next line"

 

Find The Size of  an Array

The largest available subscript for the indicated dimension of an array can be obtained by using the Ubound function.  In our one-dimensional array example, Ubound(arr) is 5.

In our two-dimensional array example above, there are two upper bound figures - both are 2.  UBound returns the following values for an array with these dimensions*:

         Dim A(1 To 100, 0 To 3, -3 To 4)

          Statement Return Value  

         UBound(A, 1)                         100                  

         UBound(A, 2)                            3

         UBound(A, 3)                            4

* Example taken from Excel VBA Help section.

The UBound function is used with the LBound function to determine the size of an array. Use the LBound function to find the lower limit of an array dimension.

          Statement Return Value  

         LBound(A, 1)                            1                  

         LBound(A, 2)                            0

         LBound(A, 3)                           -3

To get the size of an array, use the following formula:

        UBound(Arr) - LBound(Arr) + 1 For example:

        Ubound(A,1) - LBound(A,1) + 1

        = 100 - 1 + 1

        = 100

        Ubound(A,2) - LBound(A,2) + 1

        = 3 - 0 + 1

        = 4

        Ubound(A,3) - LBound(A,3) + 1

        = 4 - (-3) + 1

        = 8

For more information on arrays checkMicrosoft Support

 

Decision Structures - IF and Select Case

IF Then Statement

The IF Then is a single condition and run a single statement or a block of statement.

Example, the following statement set variable Status to "Adult" if the statement is true:

        If Age >= 18 Then Status = "Adult"

You can also use multiple-line block in the If statement as followed:

        If Ago >= 18 Then

            Status = "Adult"

            Vote = "Yes"

        End If

Note that in the multiple-line block case, End If statement is needed, where the single-line case does not.

 

IF Then Else

The If Then Else statement is used to define two blocks of conditions - true and false.

Example:

     If Age >=22 Then

        Drink = "Yes"

    Else

        Drink = "No"

    End If

Again, note that End If statement is needed in this case as well since there is more than one block of statements.

 

IF Then ElseIf

The IF Then ElseIf is used to test additional conditions without using new If Then statements.

For Example:

   If Age >= 18 and Age < 22 Then

        Msgbox "You can vote"

    ElseIf Age >=22 and Age < 62 Then

        Msgbox "You can drink and vote"

    ElseIf Age >=62 Then

        Msgbox "You are eligible to apply for Social Security Benefit"     Else

        Msgbox "You cannot drink or vote"     End If

Note that the last condition under Else is, implicitly, Age < 18.

 

Select Case

Select Case statement is an alternative to the ElseIf statement.  This method is more efficient and readable in coding the the If Then ElseIf statment. 

Example:

    Select Case Grade         Case Is >= 90

            LetterGrade = "A"         Case Is >= 80

            LetterGrade = "B"         Case Is >= 70

            LetterGrade = "C"

        Case Is >= 60

            LetterGrade = "D"

        Case Else

            LetterGrade = "Sorry"

    End Select

 

Loop Structures

For Next

Use For Next loop if the number of loops is already defined and known.  A For Next loop uses a counter variable that increases or decreases in value during each iteration of the loop.  This loop structure is being used the most for our examples on this site. 

Here is an example of the For Next loop:

    For i = 1 to 10

        Cells(i, 1) = i

    Next i

In this example, i is the counter variable from 1 to 10. The looping process will send value to the first column of the active sheet and print i (which is 1 to 10) to row 1 to 10 of that column.

Note that the counter variable, by default, increases by an increment of 1.

 

For Next Loop With Step

You can use the Step Keyword to sepcify a different increment for the counter variable. 

For example:

For i = 1 to 10 Step 2

        Cells(i, 1) = i     Next i

This looping process will print values with an increment of 2 on row 1, 3, 5, 7 and 9 on column one.

You can also have decrement in the loop by assign a negative value afte the Step keyword. 

For example:

    For i = 10 to 1 Step -2

        Cells(i, 1) = i

    Next i

This looping process will print values with an increment of -2 starts from 10 on row  10, 8, 6, 4 and 2 on column one.

 

Do While Loop

You can use the Do While Loop to test a condition at the start of the loop.  It will run the loop as long as the condition is ture and stops when the condition becomes false.  For Example:

   i = 1

    Do While i =< 10

        Cells(i, 1) = i         i = i + 1     Loop

This looping process yields the same result as in the For Next structures example.

One thing to be caution is that sometimes the loop might be a infinite loop.  And it happens when the condition never beomes false.  In such case, you can stop the loop by press [ESC] or [CTRL] + [BREAK].

 

Do Until Loop

You can test the condition at the beginning of the loop and then run the loop until the test condition becomes true.

Example:

    i = 1

    Do Until i = 11         Cells(i, 1) = i

        i = i + 1        Loop

This looping process yields the same result as in the For Next structures example.

 

Do Loop While

When you want to make sure that the loop will run at least once, you can put the test at the end of loop.  The loop will stop when the condition becomes false.   (compare this loop structure to the Do While Loop.)

For Example:

   i = 1

    Do

        Cells(i, 1) = i         i  = i + 1

    Loop While i < 11

This looping process yields the same result as in the For Next structures example.   

 

Do Loop Until

This loop structure, like the Do Loop While, makes sure that the loop will run at least once, you can put the test at the end of loop.  The loop will stop when the condition becomes true.   (compare this loop structure to the Do Until Loop.)

For Example:

   i = 1

    Do

        Cells(i, 1) = i         i  = i + 1

    Loop Until i = 11

This looping process yields the same result as in the For Next structures example.   

 

Sorting Numbers In an Array

Sorting plays a very importance role in simulation.  The sorting procedure in this example is used in many ot the tutorial on this site.  The following provides an example on how to call the Sorting sub procedure, passes the array to it, and returns the array with sorted elements.

The sub getSort procedure calls the Sort sub procedure, pass arr( ) to it, and then get a sorted array back.  The two message boxes are used to display the array before and after sorting.

   This message box shows the array before sorting

This message box shows the array after sorting

Sub getSort( )

    Dim arr(5) As Integer

    Dim str As String

    arr(1) = 8     arr(2) = 4     arr(3) = 3 arr(4) = 7     arr(5) = 2     str = ""

    For i = 1 To 5         str = str & arr(i) & vbCrLf

    Next i

    MsgBox "Before Sorting" & vbCrLf & str

    Call Sort(arr)

    str = ""     For i = 1 To 5         str = str & arr(i) & vbCrLf

    Next i

    MsgBox "After Sorting" & vbCrLf & str  

 End Sub

Sub Sort(arr( ) As Integer)

    Dim Temp As Double

    Dim i As Long

    Dim j As Long

    For j = 2 To UBound(arr)

        Temp = arr(j)

        For i = j - 1 To 1 Step -1 If (arr(i) <= Temp) Then GoTo 10             arr(i + 1) = arr(i)         Next i         i = 0 10 arr(i + 1) = Temp

    Next j

End Sub

 

Find Maximum and Minimum Values in an Array

In order to find the maximum and the minimum values in an array, the array needs to be sorted.  Once it is sorted, finding the maximum and minumum is very simple.  Using the prior example to get the maminum and the minimun, you can simplely assign the upper bound index and 1, respectively to the sorted array following:

    arr(UBound(arr)) arr(1)

Note that UBound(arr) will be 5 since there is 5 elements (start from index 1) in the array.  We use 1 as the lowest index since we did not assign any value to index 0.

The following shows the maximum and the minimum of the array.

     MsgBox "Max: " & arr(UBound(arr)) & vbCrLf & "Min:   " & arr(1) & vbCrLf

 

Double Sorting - The secret of Resampling Without Replacement

Double Sorting is the word I used for sorting one array based on the values of the second array.  This method is used when you want to get values from of a sample without select the same value twice (i.e.  the Lotto example).  The following demonstrates how this is done.



Assume you want to pick 3 people out of 8 randomly.  The challenge is that if you pick them randomly, one of the names might get picked twice or even 3 times.  To handle this challenge, the following steps can be taken:

1.   Assign random number to each of the elements in the sample (names in this case).

2.   Sort the names based on the random numbers.

As in this case, George, Chris, and Bobby are selected since they are the first 3 names after sorting.

The following shows the example using VBA codes:

Sub Resample()

    Dim i As Long

    Dim Hold(8) As Single, Hold2(8) As String

    Dim str As String

    Hold2(1) = "Anthony"

    Hold2(2) = "Bobby"

    Hold2(3) = "Chris"

    Hold2(4) = "Danny"

    Hold2(5) = "Eton"

    Hold2(6) = "Frank"

    Hold2(7) = "George"

    Hold2(8) = "Harry"

    For i = 1 To UBound(Hold)

        Hold(i) = Rnd

        Cells(i, 2) = Hhold(i)

    Next i

    Call DoubleSort(Hold, Hold2)

    str = ""

    For i = 1 To 3   

        str = str & Hold2(i) & vbCrLf

        Cells(i, 1) = Hold2(i)

    Next i

    MsgBox str

End Sub

Sub DoubleSort(x() As Single, y() As String)

    Dim xTemp As Double

    Dim yTemp As String

    Dim i As Long     Dim j As Long

    For j = 2 To UBound(x)         xTemp = x(j)         yTemp = y(j)

            For i = j - 1 To 1 Step -1

                If (x(i) <= xTemp) Then GoTo 10

                x(i + 1) = x(i)                 y(i + 1) = y(i)

            Next i i = 0

10      x(i + 1) = xTemp         y(i + 1) = yTemp

    Next j

End Sub

The DoubleSort sub procedure sorts array y (the names) based array x (the random numbers).  The Resample sub procedure retruns three unique names from the sample in a message box.

 

Excel VBA Simulation Basic Tutorial 102

This page is the second part of the Excel VBA Simulation Basic Tutorial series.  It provides Excel VBA tutorials on how to create statistic estimates that are used to analyze the data from a simulation.  Many of the examples used are already available in Excel functions.  Users can use these Excel functions as tools to check against the results that come from the examples.  These examples require basic programming skills in VBA.  Users are encouraged to read SimulationBased Tutorial 101if they have problem understanding the programming concepts and terms used on this page.

This document contains information about the following topics.

Random Number and Randomize Statement

Standard Deviation and Mean

Skewness and Kurtosis

Percentile and Confidence Interval

Profitablity

Creating a Histogram

 

Random Number and Randomize Statement

To generate random number from 0 to 1 uniformly, one can use the Rand() function in Excel or the Rnd function in VBA.  These two functions are the mother of all random numbers.  You will need either one of these functions to generate random numbers from any probability distributions.

The following example generate 5 random numbers and then display them in a message box: Sub rndNo()

    Dim str As String

    For i = 1 To 5

str = str & CStr(Rnd) & vbCrLf

    Next i

MsgBox str   

End Sub

* CStr() function converts the random numbers into string.

 

So far so good.  But when we close the file, reopen it, and run the sub routine again, the same 5 numbers come up! 

The reason why this happens is that the random numbers were actually being generated from the same set of numbers (called seed).  By placing the Randomize statement in the sub routine, the numbers will be generated from a new seed.  (Randomize uses the return value from the Timer function as the new seed value.) 

The new routine can be as followed:

Sub rndNo()

    Dim str As String

    Randomize

    For i = 1 To 5

str = str & CStr(Rnd) & vbCrLf

    Next i

MsgBox str   

End Sub

Sometimes we might want to use the same seed over and over again by just changing the values of certain variables in our simulations to see how the change affects the outcomes.  In such case, omit the Randomize statement in your sub routine.

For more information, refer to Excel VBA Help in your Excel program.

 

Standard Deviation and Mean

Standard deviaiton and mean are the two mostly used statistic estimates of all times.  Mean is the average.  Standard deviation measures the 'spreadness' of the distribution.

 

The following are functions that compute mean and standard deviation.  These functions are similar to other  functions used in our examples; they take array as their arguments.

Function Mean(Arr() As Single)

     Dim Sum As Single

Dim i As Integer

    Sum = 0

    For i = 1 To UBound(Arr)

Sum = Sum + Arr(i)

    Next i

Mean = Sum / UBound(Arr) End Function

Function StdDev(Arr() As Single)

     Dim i As Integer

     Dim avg As Single, SumSq As Single

     avg = Mean(Arr)      For i = 1 To UBound(Arr)

SumSq = SumSq + (Arr(i) - avg) ^ 2

Next i

StdDev = Sqr(SumSq / (UBound(Arr) - 1))

End Function

The following sub routine reads the data in column one from row 1 to 10 (of Sheet1) into the array, calls both functions by passing the arguements to them, computes the mean (average) and the standard deviation, then returns the values in a message box.

Sub compute()

     Dim Arr(10) As Single

     Dim Average As Single

     Dim Std_Dev As Single

     For i = 1 To UBound(Arr)

Arr(i) = Sheets("Sheet1").Cells(i, 1)

Next i

Average = Mean(Arr)

Std_Dev = StdDev(Arr)

     MsgBox "Average:" & vbTab & Average & vbCrLf & "StdDev :" & vbTab & Std_Dev End Sub

The figures below show the data and the result.

Similar example is also used in the examples on the VBA section. (These functions are similar to the AVERAGE() and the STDEV() functions provided by Excel.)    

Skewness and Kurtosis

Skewness measures the degree of asymmetry of a distribution.  For example, the skewness of a normal distribution is 0 since a normal distribution is symmetric.  Positive skewness indicates a distribution with an asymmetric tail extending toward more positive values, where as negative skewness extending toward more negative values.

 

Kurtosis measures the degree of peakedness or flatness of a distribution compared with normal distribution.  Positive kurtosis indicates a relatively peaked distribution.  Negative kurtosis indicates a relatively flat distribution. 

 

Often, these two estimates along with mean and standard deviation are used to test to see if the simulated data from a distribution is sound (if the data represents the distribution).

The following sub routine, compute(), reads the following data in column one from row 1 to 10 (of the active sheet) into the array,

 

calls both functions by passing the arguements, computes the four moments (namely mean, standard deviation, skewness, and kurt) and returns the values in a message box.

Sub compute()

    Dim arr(10) As Single

    For i = 1 To 10         arr(i) = Cells(i, 1)

    Next i

    MsgBox "Mean:" & vbTab & Format(Mean(arr), "0.0000") & vbCrLf & _

"SD:" & vbTab & Format(Var(arr) ^ 0.5, "0.0000") & vbCrLf & _

"Skew:" & vbTab & Format(Skew(arr), "0.0000") & vbCrLf & _

"Kurt:" & vbTab & Format(Kurtosis(arr), "0.0000")   

End Sub

Function Skew(arr() As Single)

    Dim i As Long, n As Long

    Dim avg As Single, sd As Single, SumTo3 As Single

    n = UBound(arr)     avg = Mean(arr)

    sd = (Var(arr)) ^ 0.5

SumTo3 = 0

    For i = 1 To n

SumTo3 = SumTo3 + ((arr(i) - avg) / sd) ^ 3

    Next i

Skew = SumTo3 * (n / ((n - 1) * (n - 2)))  End Function

Function Kurtosis(arr() As Single)

    Dim i As Long, n As Long

    Dim avg As Single, sd As Single, SumTo3 As Single

    n = UBound(arr)     avg = Mean(arr)     sd = (Var(arr)) ^ 0.5

SumTo4 = 0

    For i = 1 To n

SumTo4 = SumTo4 + ((arr(i) - avg) / sd) ^ 4

    Next i

    Kurtosis = SumTo4 * (n * (n + 1) / ((n - 1) * (n - 2) * (n - 3))) - (3 * (n - 1) ^ 2 / ((n - 2) * (n - 3))) End Function

Function Mean(arr() As Single)

    Dim Sum As Single

    Dim i As Long, k As Long

    k = UBound(arr)     Sum = 0

    For i = 1 To k

        Sum = Sum + arr(i)

    Next i

    Mean = Sum / k   

End Function

Function Var(arr() As Single)

    Dim i As Long

    Dim avg As Single, SumSq As Single

    k = UBound(arr)     avg = Mean(arr)

    For i = 1 To k

        SumSq = SumSq + (arr(i) - avg) ^ 2

    Next i

Var = SumSq / (k - 1)    End Function

The figures below show the data and the result.

 

Percentile and Confidence Interval

Percentile returns the k-th percentile of values in a range.  A confidence interval is the interval between two percentiles.  For example: if a set of data has 20 numbers ranging from 2.5 to 50 with an increment of 2.5 (2.5, 5, ., 50), the 80th percentile would be 40.  This means that 80% of the elements from the set will be equal to or below than 40. If the alpha value is 10%, for a two tails test, the lower percentile should be set to 5% (alpha/2) and the upper percentile should be set to 95% (1 - alpha/2).

In order to get the percentile, the data needs to be sorted.  In the sub routine (GetPercentile()) below, 10 random numbers between 1 to 50 are assigned to an array.  The sub routine calls the percertile function (u_percentile()).  The function calls the Sort sub routine to sort the array.  The function gets the value from the array based on the percentile (40%), and returns the percentile value back to the sub routine. 

Notice that ((Int(k * n), n), 1) in the percentile function makes sure that first, the array index is an integer and second, the maximum value and the minimum value for the array index will not excess the number of elements in the data set or below 1, respectively.

The data and the result are as followed:

 

The numbers in blue are below the 40% percentile.  Nineteen (19), in this case, is the value that the function returns at 40% percentile.

Here is the complete program for the above example:

Sub GetPercentile()

    Dim arr(10) As Single

    For i = 1 To 10

arr(i) = Int(Rnd * 50) + 1

Cells(i, 1) = arr(i)

Next i

Cells(10, 2) = u_percentile(arr, 0.4) End Sub

Function u_percentile(arr() As Single, k As Single)

    Dim i As Integer, n As Integer

    n = UBound(arr)        Call Sort(arr)

    x = ((Int(k * n), n), 1)     u_percentile = arr(x)

End Function

Sub Sort(ByRef arr() As Single)

    Dim Temp As Single

    Dim i As Long

    Dim j As Long

    For j = 2 To UBound(arr)

Temp = arr(j)

For i = j - 1 To 1 Step -1

If (arr(i) <= Temp) Then GoTo 10             arr(i + 1) = arr(i)

Next i

i = 0

10 arr(i + 1) = Temp

If j Mod 100 = 0 Then

Cells(26, 5) = j

End If

    Next j

End Sub Similar concept from this tutorial is used in many of our simulation examples.

(This function is similar to the PERCENTILE() and the QUARTILE() functions provided by Excel.) Profitablity

The previous percentile example shows how to get the value that corresponds to a specific percentile. In this example, we will show you on how to get the percentile with a given value.

We are going to start this tutorial by showing you a very simple simulation.  However, simulation is not necessary to get the answer in this example because we are using very loss assumptions.  The result can actually be computed in your head if your math is that good.

Assume your profit is distributed uniformly.  From the past records, you know that your annual average profit flucturates between -$100,000 to $500,000.  We want to know what is the probabilty that you will be making over $300,000 next year holding all other things constant.  Interesting enough?  Now watch this:

            1 - (300,000-(-100,000))/(500,000-(-100,000)) = 1 - 0.666 = 0.333

The probabilty will be 33%.

Now, let's run the simulation and see what will happen.

Five simulations were ran, each with 1000 iterations.  The result shows 5 probability values in a message box.  Each result is closed to the mathematic computation of 33%.

 

Here is the sub routine that runs the simulation:

Sub GetProb()

    Dim high As Single, low As Single, profit As Single

    Dim counter As Integer

    Dim str As String

    high = 500000     low = -100000     profit = 300000

    srt = ""     For j = 1 To 5         counter = 0         For i = 1 To 1000

If profit <= Rnd * (high - low + 1) + low Then                 counter = counter + 1

End If         Next i

str = str & counter / 1000 & vbCrLf

    Next j

    MsgBox str End Sub

This example is also implemented in the Monte Carlo Simulationtutorial.

(This function is similar to the PERCENTRANK() function provided by Excel.)  

 

Creating a Histogram

A histogram from a simulation shows the graphical representation of the derived probability distribution. 

The following sub procedure is an improved model for generating a histogram.  The first parameter, M, is the number of bins (breaks) that you want to have for the histogrm.  The second parameter is the array that contains that values for the histogram.

In order for this procedure to work properly, the array needs to be sorted for calling the histogram procedure.  This way, the maximum and the minimum values can be derived and used for setting up the bin values. Please see the following examples for the implementation:

Normal Distribution Random Number Generator, Bootstrap - A Non-Parametric Approach, and Monte Carlo Simulation.

Here are the codes that generate a histogram:

Sub Hist(M As Long, arr() As Single)

    Dim i As Long, j As Long

    Dim Length As Single

ReDim breaks(M) As Single

ReDim freq(M) As Single

For i = 1 To M         freq(i) = 0     Next i

Length = (arr(UBound(arr)) - arr(1)) / M

    For i = 1 To M

breaks(i) = arr(1) + Length * i

    Next i

    For i = 1 To UBound(arr)

If (arr(i) <= breaks(1)) Then freq(1) = freq(1) + 1

        If (arr(i) >= breaks(M - 1)) Then freq(M) = freq(M) + 1

For j = 2 To M - 1

If (arr(i) > breaks(j - 1) And arr(i) <= breaks(j)) Then freq(j) = freq(j) + 1         Next j

    Next i

    For i = 1 To M

Cells(i, 1) = breaks(i)

Cells(i, 2) = freq(i)

Next i End Sub

The following is an example output from the procedure:

The class is the bins or the breaks.  The frequency contains the number of simulated values for each of the classes.

Here is the histogram chart from this example:

 

Excel VBA Statistics and Mathematics Examples

This page contains simple Excel VBA Statistics and Mathematics examples.  Many of the examples used are already available in functions that come with Excel.  Users can use these Excel functions as tools to check against the results that come from the examples.  These examples require basic programming skills in VBA.  Users are encouraged to read the Simulation Based Tutorial 101if they have problem understanding the programming concepts and terms used on this page.

This document contains information about the following topics.

Finding Median

Generate Random Numbers From Uniform Distribution

Sum Numbers

Compute Factorial

Binomial Coefficient

Cumulative Standard Normal Distribution

 

Finding Median

To find the median from an array, two steps are required. First the array needs to be sorted (in either order), then a decision structure needs to be used.

Step 1.  Sort the array. See example on sorting.

Step 2.  If the total elements in the array is an odd number (defined by Ubound(Arr) Mod = 1), then the median is the middle number (defined by Arr(Int(Ubound(Arr) / 2) + 1)).              If the total elements in the array is an even number then take the average of the two middle              numbers.

Function u_median(Arr() As Single)    Call Sort(Arr)

    If UBound(Arr) Mod 2 = 1 Then

u_median = Arr(Int(UBound(Arr) / 2) + 1)     Else

u_median = (Arr(UBound(Arr) / 2) + Arr(Int(UBound(Arr) / 2) + 1)) / 2     End If

    End Function  

This function is also implemented in the Bootstrap - A Non-Parametric Approachexample.

(This function is similar to the MEDIAN() function provided by Excel.)           

 

Generate Random Numbers From Uniform Distribution

This function provides an uniform distribution random number between a specified range. 

Function UniformRandomNumner(Low As Single, High As Single)

UniformRandomNumner = Rnd * (High - Low + 1) + Low

End Function

For example, the following function returns a random number between 10 and 100:

UniformRandomNumner(10, 100)

(This function is similar to the RANDBETWEEN() function provided by Excel.)  

 

Sum Numbers

This function reads an array, and then returns the total number of the elements in the array.

Function u_sum(Arr() As Single)

    For i = 1 To UBound(Arr)         u_sum = u_sum + Arr(i)

    Next i

End Function

Here is a sub routine that calls the u_sum function and returns the sum in a message box.

Sub computeSum()

    Dim arr(3) As Single

arr(1) = 5     arr(2) = 4     arr(3) = 10

    MsgBox u_sum(arr)

End Sub

The message box will return 19.

(This function is similar to the SUM() function provided by Excel.)     

 

Compute Factorial

To initiate the loop,  we assign u_fact, the function, an initial value of 1.  Then we multiple the new number (i) with the current number (u_fact) until i = Int(number).  Note that the Int function is require to make sure the number is an integer or becomes an integer.

Function u_fact(number As Single)     u_fact = 1

    For i = 1 To Int(number)         u_fact = u_fact * i

    Next i

End Function

For example, the following function returns a 6: u_fact(3)

(This function is similar to the FACT() function provided by Excel.) 

 

Dim i As Integer           Dim b As Double           b = 1

For i = 0 To j - 1

b = b * (n - i) / (j - i)           Next i

u_binoCoeff = b

End Function

The following function compute all the possible combination on 5 items choosen from 10 items.  This function returns 252: u_binoCoeff(5, 10)

This function is also implemented in the example.

(This function is similar to the COMBIN() function provided by Excel.)     

 

Cumulative Standard Normal Distribution

This function computes the area under the left hand side of a specified value (the z value) from a standard normal distribution density function curve.  In plain English, it returns the probabilty of  X that is smaller than a specific value.

If you do not know what a normal curve looks like or have already forgotten about it, here is a sample:

In this example, the probabilty of X smaller than 1.64 (z) is 94.9497%.  Function u_SNorm(z)

    c1 = 2.506628     c2 = 0.3193815     c3 = -0.3565638     c4 = 1.7814779     c5 = -1.821256     c6 = 1.3302744     If z > 0 Or z = 0 Then               w = 1

Else: w = -1     End If

    y = 1 / (1 + 0.2316419 * w * z)

u_SNorm = 0.5 + w * (0.5 - (Exp(-z * z / 2) / c1) * _             (y * (c2 + y * (c3 + y * (c4 + y * (c5 + y * c6))))))

End Function u_SNorm(1.64) = 0.949497

This function is also implemented in the Putexample.

(This function is similar to the NORMSDIST() function provided by Excel.)     



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