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 Approach example.



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



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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.)



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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.)


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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.)



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Binomial Coeffieient







Function u_binoCoeff(n, j)

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 Bootstrap - A Non-Parametric Approach example.



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


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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 Black-Scholes Option Pricing Model - European Call and Put example.



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



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