Standard Normal Distribution (SND) – Java Program

The standard normal distribution is a special case of the normal distribution. It occurs when a normal random variable has a mean of 0 and a standard deviation of 1. The normal random variable of a standard normal distribution is called a standard score or a z score.
A conversion from Normally distributed to Standard Normally distributed value occurs via the formula,

Z = (X - u) / s
where:
Z = value on the standard normal distribution
X = value on the original distribution
u = mean of the original distribution
s = standard deviation of the original distribution

Code –

// Java code to demonstrate the naive method
// of finding Z-value

import java.io.*;
import java.util.*;

class SDN {
    public static void main(String[] args)
    {

        // initialization of variables
        double Z, X, s, u;
        X = 26;
        u = 50;
        s = 10;

        // master formula
        Z = (X - u) / s;

        // print the z-value
        System.out.println("the Z-value obtained is: " + Z);
    }
}

Output –

the Z-value obtained is: -2.4

Generating a Random Standard Normal Function – Using nextGaussian() in Java :
The nextGaussian() method is used to get the next random, Normally distributed double value with mean 0.0 and standard deviation 1.0.

Declaration :
public double nextGaussian()
Parameters :
NA
Return Value :
The method call returns the random, Normally distributed double value
with mean 0.0 and standard deviation 1.0.
Exception :
NA

The following example shows the usage of java.util.Random.nextGaussian():

Code –

// Java code to demonstrate the working
// of nextGaussian()
import java.util.*;

public class NextGaussian {

    public static void main(String[] args)
    {

        // create random object
        Random ran = new Random();

        // generating integer
        double nxt = ran.nextGaussian();

        // Printing the random Number
        System.out.println("The next Gaussian value generated is : " + nxt);
    }
}

Output –

The next Gaussian value generated is : -0.24283691098606316