Properties of Gaussian Distribution
Some of the important properties are
- The Gaussian distribution must be symmetric around its mean with same probability density on both sides of mean.
- The sum of many independent, identically distributed random variables converges to a Gaussian distribution.
- When you estimate the mean and variance of a Gaussian distribution from a set of data, the maximum likelihood estimators provide the most accurate estimates compared to other distributions.
- In linear transformations, if X follows a Gaussian distribution, then aX+b also follows a Gaussian distribution for constants a and b. This property makes the Gaussian distribution robust and convenient for modeling various real-world phenomena that involve linear transformations.
- In multiple dimensions, the Gaussian distribution extends naturally. It describes how multiple variables can be jointly Gaussian, meaning that any linear combination of these variables also follows a Gaussian distribution. This property is valuable for modeling complex systems with multiple interacting variables.
Gaussian Distribution In Machine Learning
The Gaussian distribution, also known as the normal distribution, plays a fundamental role in machine learning. It is a key concept used to model the distribution of real-valued random variables and is essential for understanding various statistical methods and algorithms.
Table of Content
- Gaussian Distribution
- Gaussian Distribution Curve
- Gaussian Distribution Table
- Properties of Gaussian Distribution
- Machine Learning Methods that uses Gaussian Distribution
- Implementation of Gaussian Distribution in Machine Learning