What is the Difference Between Gaussian and Normal Distribution?

The terms "Gaussian distribution" and "normal distribution" are often used interchangeably in statistics, and there is no significant difference between the two. Both refer to a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In graphical form, the Gaussian or normal distribution appears as a "bell curve".

To summarize:

• A Gaussian distribution, also known as a normal distribution, is a probability distribution that is symmetric about the mean.
• The width of the curve is defined by the standard deviation, and the mean and standard deviation are used to determine the shape of the distribution.
• The Gaussian or normal distribution has the same general shape: symmetric and unimodal (i.e., a single peak).
• Some authors may differentiate between the two, with "Gaussian distribution" referring to any distribution with a bell-shaped curve and "normal distribution" referring specifically to the standard normal distribution (with mean 0 and standard deviation 1). However, this distinction is not universally adopted, and the terms are often used synonymously.

Comparative Table: Gaussian vs Normal Distribution

The terms "Gaussian" and "Normal" distributions are often used interchangeably in statistics, as they refer to the same probability distribution. The Gaussian distribution, also known as the Normal distribution, is a continuous, symmetric distribution that appears as a "bell curve" in graphical form. It plays a central role in statistics and is commonly used to model various phenomena, such as measurement errors and the distribution of heights in a population.

Here is a summary of the differences and similarities between Gaussian and Normal distributions:

A specific instance of the Normal distribution is the Standard Normal Distribution, which has a mean of 0 and a standard deviation of 1. This distribution is often used as a reference point for comparing other Normal distributions.