' 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 
' This example of Random.Sample() generates the following output:
'    The derived RandomProportional class overrides the Sample method to
'    generate random numbers in the range [0.0, 1.0]. The distribution
'    of the numbers is proportional to their numeric values. For example,
'    numbers are generated in the vicinity of 0.75 with three times
'    the probability of those generated near 0.25.
'    
'    Random doubles generated with the NextDouble( ) method:
'    
'      0.28377004  0.75920598  0.33430371  0.66720626  0.97080243  0.27353772
'      0.17787962  0.54618410  0.08145080  0.56286100  0.99002910  0.64898614
'      0.27673277  0.99455281  0.93778966  0.76162002  0.70533771  0.44375798
'      0.55939883  0.87383136  0.66465779  0.77392566  0.42393411  0.82409159
'    
'    Random integers generated with the Next( ) method:
'    
'      1364479914  1230312341  1657373812  1526222928   988564704   700078020
'      1801013705  1541517421  1146312560   338318389  1558995993  2027260859
'       884520932  1320070465   570200106  1027684711   943035246  2088689333
'       630809089  1705728475  2140787648  2097858166  1863010875  1386804198
'    
'    To demonstrate the proportional distribution, 1,000,000 random
'    integers and doubles are grouped into 10 equal value ranges. This
'    is the count of values in each range:
'    
'            Integer Range     Count        Double Range     Count
'            -------------     -----        ------------     -----
'             0- 214748363     9,892     0.00000-0.10000     9,928
'     214748364- 429496728    30,341     0.10000-0.20000    30,101
'     429496729- 644245093    49,958     0.20000-0.30000    49,964
'     644245094- 858993458    70,099     0.30000-0.40000    70,213
'     858993459-1073741823    90,801     0.40000-0.50000    89,553
'    1073741824-1288490187   109,699     0.50000-0.60000   109,427
'    1288490188-1503238552   129,438     0.60000-0.70000   130,339
'    1503238553-1717986917   149,886     0.70000-0.80000   150,000
'    1717986918-1932735282   170,338     0.80000-0.90000   170,128
'    1932735283-2147483647   189,548     0.90000-1.00000   190,347

using System;

// This derived class converts the uniformly distributed random 
// numbers generated by base.Sample( ) to another distribution.
public class RandomProportional : Random
{
    // The Sample method generates a distribution proportional to the value 
    // of the random numbers, in the range [0.0, 1.0].
    protected override double Sample( )
    {
        return Math.Sqrt( base.Sample( ) );
    }

    public override int Next()
    {
       return (int) (Sample() * int.MaxValue);
    }   
}

public class RandomSampleDemo  
{
    static void Main( )
    {    
        const int rows = 4, cols = 6;
        const int runCount = 1000000;
        const int distGroupCount = 10;
        const double intGroupSize = 
            ( (double)int.MaxValue + 1.0 ) / (double)distGroupCount;

        RandomProportional randObj = new RandomProportional( );

        int[ ]      intCounts = new int[ distGroupCount ];
        int[ ]      realCounts = new int[ distGroupCount ];

        Console.WriteLine( 
            "\nThe derived RandomProportional class overrides " +
            "the Sample method to \ngenerate random numbers " +
            "in the range [0.0, 1.0]. The distribution \nof " +
            "the numbers is proportional to their numeric values. " +
            "For example, \nnumbers are generated in the " +
            "vicinity of 0.75 with three times the \n" +
            "probability of those generated near 0.25." );
        Console.WriteLine( 
            "\nRandom doubles generated with the NextDouble( ) " +
            "method:\n" );

        // Generate and display [rows * cols] random doubles.
        for( int i = 0; i < rows; i++ )
        {
            for( int j = 0; j < cols; j++ )
                Console.Write( "{0,12:F8}", randObj.NextDouble( ) );
            Console.WriteLine( );
        }

        Console.WriteLine( 
            "\nRandom integers generated with the Next( ) " +
            "method:\n" );

        // Generate and display [rows * cols] random integers.
        for( int i = 0; i < rows; i++ )
        {
            for( int j = 0; j < cols; j++ )
                Console.Write( "{0,12}", randObj.Next( ) );
            Console.WriteLine( );
        }

        Console.WriteLine( 
            "\nTo demonstrate the proportional distribution, " +
            "{0:N0} random \nintegers and doubles are grouped " +
            "into {1} equal value ranges. This \n" +
            "is the count of values in each range:\n",
            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( int i = 0; i < runCount; i++ )
        {
            intCounts[ (int)( (double)randObj.Next( ) / 
                intGroupSize ) ]++;
            realCounts[ (int)( randObj.NextDouble( ) * 
                (double)distGroupCount ) ]++;
        }

        // Display the count of each group.
        for( int i = 0; i < distGroupCount; i++ )
            Console.WriteLine( 
                "{0,10}-{1,10}{2,10:N0}{3,12:N5}-{4,7:N5}{5,10:N0}",
                (int)( (double)i * intGroupSize ),
                (int)( (double)( i + 1 ) * intGroupSize - 1.0 ),
                intCounts[ i ],
                ( (double)i ) / (double)distGroupCount,
                ( (double)( i + 1 ) ) / (double)distGroupCount,
                realCounts[ i ] );
    }
}

/*
This example of Random.Sample() displays the following output:

   The derived RandomProportional class overrides the Sample method to
   generate random numbers in the range [0.0, 1.0). The distribution
   of the numbers is proportional to the number values. For example,
   numbers are generated in the vicinity of 0.75 with three times the
   probability of those generated near 0.25.

   Random doubles generated with the NextDouble( ) method:

     0.59455719  0.17589882  0.83134398  0.35795862  0.91467727  0.54022658
     0.93716947  0.54817519  0.94685080  0.93705478  0.18582318  0.71272428
     0.77708682  0.95386216  0.70412393  0.86099417  0.08275804  0.79108316
     0.71019941  0.84205103  0.41685082  0.58186880  0.89492302  0.73067715

   Random integers generated with the Next( ) method:

     1570755704  1279192549  1747627711  1705700211  1372759203  1849655615
     2046235980  1210843924  1554274149  1307936697  1480207570  1057595022
      337854215   844109928  2028310798  1386669369  2073517658  1291729809
     1537248240  1454198019  1934863511  1640004334  2032620207   534654791

   To demonstrate the proportional distribution, 1,000,000 random
   integers and doubles are grouped into 10 equal value ranges. This
   is the count of values in each range:

           Integer Range     Count        Double Range     Count
           -------------     -----        ------------     -----
            0- 214748363    10,079     0.00000-0.10000    10,148
    214748364- 429496728    29,835     0.10000-0.20000    29,849
    429496729- 644245093    49,753     0.20000-0.30000    49,948
    644245094- 858993458    70,325     0.30000-0.40000    69,656
    858993459-1073741823    89,906     0.40000-0.50000    90,337
   1073741824-1288490187   109,868     0.50000-0.60000   110,225
   1288490188-1503238552   130,388     0.60000-0.70000   129,986
   1503238553-1717986917   149,231     0.70000-0.80000   150,428
   1717986918-1932735282   170,234     0.80000-0.90000   169,610
   1932735283-2147483647   190,381     0.90000-1.00000   189,813
*/