gaussian

Thân thiện

A scientist plots a Gaussian distribution on a graph.

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.

Học thuật

Adjective

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

Từ đồng nghĩa

• gaussian