Generate random weighted variables

In this post I describe the common problem how to generate random weighted variables. For example you have a die with 6 faces that is fixed, so the probability of an 1 is not the same with the probability of a 2 etc.

The table below shows an example:

Face Probability
1  25
2  25
3  20
4  20
5  5
6  5

One easy solution is to reduce the problem to another one with a die with 100 faces that is not fixed.

You generate a random value from 0-99 that follows the uniform distribution. Do not use the modulo function to do that. See this post instead.

Once you have that value you perform the following steps:

You check the space within which that value relies.

  1. between 0 and 24, you generate 1 as the weighted variable
  2. between 25 and 49, you generate 2 as the weighted variable
  3. between 50 and 69, you generate 3 as the weighted variable
  4. between 70 and 89, you generate 4 as the weighted variable
  5. between 90 and 94, you generate 5 as the weighted variable
  6. between 95 and 99, you generate 6 as the weighted variable

 

 

 

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Generate uniformly distributed random variables

Formulas shown below generate values that follow uniform distribution.

Using simple modulo methods is not considered as a good solution (although used a lot by students) as the module function does not generate all the variables with the same frequency.

Random integer between [ 0, 1 ]

int r = (int) (rand()/(RAND_MAX + 0.0));

Random integer between [ 0, 1 )

int r = (int) (rand()/(RAND_MAX + 1.0));

Random integer between [ 0, N ]

int r = (int) (N * (rand() / (RAND_MAX + 0.0)));

Random integer between [ 0, N )

int r = (int) (N * (rand()/(RAND_MAX + 1.0)));

Random integer between [ M, N ]

int r = (int) (Μ + (rand()/(RAND_MAX + 0.0))*(N-M+1));

Random integer between [ M, N )

int r = (int) (Μ + (rand()/(RAND_MAX + 1.0))*(N-M+1));

Summary

The general formula is:

int r = (int) (A + (rand()/(RAND_MAX + C))*B);

Values of M, N, K are shown in the following table:

Range A B  C
 [ 0, 1 ]  0  1  0.0
 [ 0, N ]  0  N  0.0
 [ M, N ]  M  N – M + 1  0.0
 [ 0, 1 )  0  1  1.0
 [ 0, N )  0  N  1.0
 [ M, N )  M  N – M + 1  1.0

Generating values of normal distribution – Marsaglia method

Assuming you can already produce variables of uniform distribution, you can produce variables of normal distribution using various formulas. Two of the most important are:

  1. Box–Muller method
  2. Marsaglia polar method

Most methods are based on Box-Muller method.

The Marsaglia method is my favorite since it does not require using sin() or cos() functions and the steps are very easy to implement.

Here is a sequence of the steps:

  1. Generate a value that follows uniform distribution in any space you want (eg: [ 0 , 1 ))
  2. Map that value to space (-1, +1) and assign it to variable U
  3. Repeat steps 1 and 2 and assign the result to variable V
  4. Calculate S = U*U + V*V
  5. if S = 0 or S >= 1 then free all variables if needed and restart from the beginning
  6. The following two variables will be independent and standard normally distributed (mean = 0, variance = 1):

marsaglia

Optionally you can add m to the quantities above to change the mean value of the distribution.

 

Java – Appending objects to binary files

Java is tricky, you cannot add objects to already existent files with default classes.

Here is the solution:

import java.io.EOFException;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.ObjectInputStream;
import java.io.ObjectOutputStream;
import java.io.OutputStream;

public class Test{
    private static String filename = "test";

    public static void main(String[] args) {
        writeToBinary (filename, "a", true);
        writeToBinary (filename, "b", true);
        writeToBinary (filename, "c", true);
        readFromBinaryFile (filename);
    }

    public static void writeToBinary (String filename, Object obj, boolean append){
        File file = new File (filename);
        ObjectOutputStream out = null;

        try{
            if (!file.exists () || !append) out = new ObjectOutputStream (new FileOutputStream (filename));
            else out = new AppendableObjectOutputStream (new FileOutputStream (filename, append));
            out.writeObject(obj);
            out.flush ();
        }catch (Exception e){
            e.printStackTrace ();
        }finally{
            try{
                if (out != null) out.close ();
            }catch (Exception e){
                e.printStackTrace ();
            }
        }
    }

    public static void readFromBinaryFile (String filename){
        File file = new File (filename);

        if (file.exists ()){
            ObjectInputStream ois = null;
            try{
                ois = new ObjectInputStream (new FileInputStream (filename));
                while (true){
                    String s = (String)ois.readObject ();
                    System.out.println (s);
                }
            }catch (EOFException e){

            }catch (Exception e){
                e.printStackTrace ();
            }finally{
                try{
                    if (ois != null) ois.close();
                }catch (IOException e){
                    e.printStackTrace ();
                }
            }
        }
    }

    private static class AppendableObjectOutputStream extends ObjectOutputStream {
          public AppendableObjectOutputStream(OutputStream out) throws IOException {
            super(out);
          }

          @Override
          protected void writeStreamHeader() throws IOException {}
    }
}

 

References:

https://stackoverflow.com/questions/4646272/appending-objects-to-a-binary-file

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