' This derived class converts the uniformly distributed random 
' numbers generated by base.Sample( ) to another distribution.
Public Class RandomProportional
   Inherits Random

   ' The Sample method generates a distribution proportional to the value 
   ' of the random numbers, in the range [0.0, 1.0].
   Protected Overrides Function Sample( ) As Double
      Return Math.Sqrt( MyBase.Sample( ) )
   End Function
   
   Public Overrides Function [Next]() As Integer
      Return Sample() * Integer.MaxValue
   End Function 
End Class 

Module RandomSampleDemo
    Sub Main( )
        Const rows As Integer = 4, cols As Integer = 6
        Const runCount As Integer = 1000000
        Const distGroupCount As Integer = 10
        Const intGroupSize As Double = _
            ( CDbl( Integer.MaxValue ) + 1.0 ) / _
            CDbl( distGroupCount )
            
        Dim randObj As New RandomProportional( )
            
        Dim intCounts( distGroupCount ) As Integer
        Dim realCounts( distGroupCount ) As Integer
        Dim i As Integer, j As Integer 
            
        Console.WriteLine( vbCrLf & _
            "The derived RandomProportional class overrides " & _ 
            "the Sample method to " & vbCrLf & _
            "generate random numbers in the range " & _ 
            "[0.0, 1.0]. The distribution " & vbCrLf & _
            "of the numbers is proportional to their numeric " & _
            "values. For example, " & vbCrLf & _ 
            "numbers are generated in the vicinity of 0.75 " & _
            "with three times " & vbCrLf & "the " & _
            "probability of those generated near 0.25." )
        Console.WriteLine( vbCrLf & _
            "Random doubles generated with the NextDouble( ) " & _ 
            "method:" & vbCrLf )
            
        ' Generate and display [rows * cols] random doubles.
        For i = 0 To rows - 1
            For j = 0 To cols - 1
                Console.Write( "{0,12:F8}", randObj.NextDouble( ) )
            Next j
            Console.WriteLine( )
        Next i
            
        Console.WriteLine( vbCrLf & _
            "Random integers generated with the Next( ) " & _ 
            "method:" & vbCrLf )
            
        ' Generate and display [rows * cols] random integers.
        For i = 0 To rows - 1
            For j = 0 To cols - 1
                Console.Write( "{0,12}", randObj.Next( ) )
            Next j
            Console.WriteLine( )
        Next i
            
        Console.WriteLine( vbCrLf & _
            "To demonstrate the proportional distribution, " & _ 
            "{0:N0} random " & vbCrLf & _
            "integers and doubles are grouped into {1} " & _ 
            "equal value ranges. This " & vbCrLf & _
            "is the count of values in each range:" & vbCrLf, _
            runCount, distGroupCount )
        Console.WriteLine( "{0,21}{1,10}{2,20}{3,10}", _
            "Integer Range", "Count", "Double Range", "Count" )
        Console.WriteLine( "{0,21}{1,10}{2,20}{3,10}", _
            "-------------", "-----", "------------", "-----" )
            
        ' Generate random integers and doubles, and then count 
        ' them by group.
        For i = 0 To runCount - 1
            intCounts( Fix( CDbl( randObj.Next( ) ) / _
                intGroupSize ) ) += 1
            realCounts( Fix( randObj.NextDouble( ) * _
                CDbl( distGroupCount ) ) ) += 1
        Next i
            
        ' Display the count of each group.
        For i = 0 To distGroupCount - 1
            Console.WriteLine( _
                "{0,10}-{1,10}{2,10:N0}{3,12:N5}-{4,7:N5}{5,10:N0}", _
                Fix( CDbl( i ) * intGroupSize ), _
                Fix( CDbl( i + 1 ) * intGroupSize - 1.0 ), _
                intCounts( i ), _
                CDbl( i ) / CDbl( distGroupCount), _
                CDbl( i + 1 ) / CDbl( distGroupCount ), _
                realCounts( i ) )
        Next i
    End Sub
End Module