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Standard Normal Distribution (SND) – Java Program

  • Last Updated : 06 Feb, 2018

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
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 –

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// Java code to demonstrate the naive method
// of finding Z-value
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 :
Return Value :
The method call returns the random, Normally distributed double value
with mean 0.0 and standard deviation 1.0.
Exception :

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

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