There are a few reasons for choosing Normal distribution and Student-T distribution.
- They are approximately a wide variety of random variables.
- Distributions of samples mean with large enough sample sizes could be approximate to normal.
- All computable statistics are elegant.
- Heavily used for regression analysis.
- It has a good track record.
The statistical term for Normal Distribution is Gaussian Distribution, But many people call it the Bell curve as it shapes like a bell. It is symmetrical and its mean, median, and mode are equal. If you remember the Skewness, you easily recognize it has no skew. It is perfectly centered around its mean. It is denoted by N. N stands for normal. also, it has a formula which is written below.
N ~ (μ, σ2)
Where,
N — Normal Distribution,
~ — Distribution
μ — mu (Mean)
𝜎2 — Sigma (variance)
It is a normally distributed histogram. Where the concentration of observation is in the middle and the mean, median, and mode are equal.
In this figure, the mean is different but σ sigma Standard deviation is the same for all. now the question is how to measure standard deviation, check the below figure.
If we reshape the graph only the standard deviation will be changed but the mean will be the same.
Standard Normal Distribution: The Standard Normal distribution is a particular case of the Normal distribution. It has a mean of 0 and a standard deviation of 1. Every Normal distribution can be ‘standardized’ using the standardization formula.
Z = x-μ/ 𝜎
A variable following the Standard Normal distribution is denoted with the letter z. also the variable is called z score.
Why standardize?
Standardization allows us to:
• compare different normally distributed datasets
• detect normality
• detect outliers
• create confidence intervals
• test hypotheses
• perform regression analysis
Every distribution can be standardized. how?
N ~ (μ, σ2) ≫ ~ N(0,1)
Standardization is a process of transforming this variable to one with a mean of Zero (0) and a standard deviation of 1. The distribution is standardized. the result is called a standard normal distribution.
Adding and subtracting values from all data points does not change the standard deviation.
From this figure, we can say by using the Z-score mean will be 0 and the standard deviation will be 1.