It is a type of continuous probability distribution for a random variable. It is also called as Normal distribution.
The general form of its probability density function is;
Here the parameter µ is the mean or expectation of the distribution and σ is the standard deviation.
When the mean becomes 0 and variance becomes 1 in a Gaussian distribution, it becomes a Standard Normal Distribution.
Gaussian distribution follows a bell-shaped curve and hence generally known as a bell curve.
Let us consider a random variable 'X' such that 'X' belongs to Gaussian distribution.
Now we look onto the empirical formula in Gaussian distribution.
• The first empirical formula is given as
i.e.,68% of the total distribution will be present in the first standard deviation range.
• The second empirical formula is given as
This means that 95% of the total distribution will be present in the second standard deviation range.
• The third empirical formula is given as
This means that 99.7% of the total distribution will be present in the third standard deviation range.
Now we look onto what is called as log-normal distribution.
Consider a random variable ‘X’ such that it has the datapoints
We say that this random variable 'X' belongs to log-normal distribution if ln(X) is normally distributed and follows the Gaussian distribution.