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
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