Standard Normal Distribution

A standard Normal Distribution is a type of distribution in which we have a mean equal to zero and Standard deviation is equal to one. The center of Standard normal distribution is 0. To make this a distribution into Standard normal distribution make sure that our distribution must be a Gaussian distribution or Normal distribution. It is the assumption of the Standard Normal Distribution Curve that data should follow Normal Distribution.

Difference between Normal Distribution and Standard Normal Distribution

Normal Distribution: It is a type of bell curve shape with the mean can be anything and the standard deviation can be anything (Depends on data). It follows the empirical formula in which the third standard deviation will cover 99.7 % of the data. It shows that most of the data is under the bell curve and makes a normal distribution. But if it shows some skewness towards the right or left side. Then we have to treat them and convert into a normal distribution before converting into standard normal distribution.

Standard Normal Distribution: It is also a bell curve but with the mean equal to 0 and the standard deviation equal to 1. It is mainly used for scaling. It helps to solve many complex problems in Machine learning like to find the probability or probability between the two intervals by using z-table.

How to convert a normal distribution into Standard Normal Distribution?

Mathematically

To convert normal distribution into Standard Normal Distribution we use z score formula. Let’s take an example we have some data points and assume that it follows a normal distribution. After that, we have to find the mean and standard deviation of the data and just put each data point in the formula and calculate standard normal distribution and make a new data set which will follow the bell curve with mean=0 and standard deviation equal to one.

How to do it with Python?

To generate a Normal Distribution in python we can use numpy.random.normal() by importing numpy library after that we can check the distribution of the data. It will follow a Normal Distribution.

For a Standard Normal Distribution, we can use numpy.random.randn(). It will generate a curve with a mean equal to zero and a standard deviation equal to 1.

I hope you Like it. If you have any queries you can ask me on Linkedin

Account Link: https://www.linkedin.com/in/harsharora0703/