Definition

1. Adjective:
   • Of or relating to Karl Gauss or his mathematical theories: Pertaining to the German mathematician Carl Friedrich Gauss, his work, or concepts derived from his contributions to fields such as mathematics, physics, and astronomy.
   • Having the characteristics of a Gaussian distribution: Describing a function, curve, or statistical distribution that follows the specific bell-shaped, symmetric form defined by Gauss, commonly known as the normal distribution.

Usage Examples

• Adjective:
  • The researcher applied a Gaussian filter to smooth the image data. (The researcher used a filter based on Gauss's mathematical principles.)
  • Noise in the signal was assumed to be Gaussian. (The unwanted variation in the signal was assumed to follow a normal distribution.)
  • Gaussian optics is a fundamental theory in the design of lenses. (This branch of optics is based on the approximations developed by Gauss.)

Advanced Usage

• "Gaussian process": In statistics and machine learning, a collection of random variables, any finite number of which have a joint Gaussian distribution.
  • Gaussian processes are used for regression and classification tasks.
• "Gaussian elimination": In linear algebra, a standard algorithm for solving systems of linear equations.
  • The student used Gaussian elimination to find the solution to the matrix equation.
• "Gaussian curvature": In differential geometry, an intrinsic measure of curvature for a surface.
  • A sphere has constant positive Gaussian curvature.

Variants and Related Words

• Gaussianity (noun): The property of being Gaussian or following a Gaussian distribution.
  • The test checks for Gaussianity in the dataset.
• Non-Gaussian (adjective): Not having the properties of a Gaussian distribution.
  • The financial returns showed a non-Gaussian, heavy-tailed distribution.

Synonyms

• Normal (in statistics): Often used interchangeably with "Gaussian" to describe the distribution.
  • The data follows a normal (Gaussian) distribution.
• Bell-curve (informal, noun): Describes the shape of the Gaussian distribution plot.

Related Phrases and Compounds

• Gaussian distribution: The full term for the normal probability distribution.
• Gaussian function: The mathematical function that defines the bell curve.
• Gaussian noise: A statistical noise having a probability density function equal to that of the normal distribution.

Adjective

1. of or relating to Karl Gauss or his mathematical theories of magnetics or electricity or astronomy or probability
   • Gaussian distribution