Gaussian shape

Học thuật
Thân thiện
Definition
  1. Noun:
    • A symmetrical curve representing the normal distribution: A "Gaussian shape" is the characteristic bell-shaped curve that describes the distribution of many natural phenomena and data sets around a mean value. It is named after the mathematician Carl Friedrich Gauss.
Usage
  • The term "Gaussian shape" is used primarily in statistics, mathematics, and various scientific fields to describe the visual form of data that follows a normal distribution.
  • It functions as a countable noun (e.g., , ).
Examples
  • Noun:
    • The data points formed a perfect Gaussian shape on the graph.
    • When plotting the results, we observed the characteristic Gaussian shape.
    • Many biological measurements, like height, approximate a Gaussian shape.
Advanced Usage
  • "To approximate a Gaussian shape": To nearly form or resemble the bell curve.
    • The sample distribution began to approximate a Gaussian shape as we collected more data.
  • "Deviate from a Gaussian shape": To not follow the standard bell curve pattern.
    • The financial returns often deviate from a Gaussian shape, showing "fat tails".
Variants and Related Words
  • Gaussian distribution (n): Another term for the normal distribution.
    • The Gaussian distribution is fundamental to statistical theory.
  • Gaussian curve (n): A direct synonym for Gaussian shape.
    • The histogram was fitted with a smooth Gaussian curve.
  • Bell curve (n): A common informal name for the Gaussian shape.
    • Student grades are sometimes assumed to follow a bell curve.
Synonyms
  • Normal curve: A curve representing a normal distribution.
  • Bell-shaped curve: A descriptive synonym emphasizing the visual form.
Related Phrases
  • Gaussian function: The mathematical equation that produces the Gaussian shape.
    • The Gaussian function includes parameters for mean and standard deviation.
  • Gaussian noise: In signal processing, noise with a Gaussian amplitude distribution.
    • The model assumes the presence of additive Gaussian noise.
Noun
  1. a symmetrical curve representing the normal distribution

Từ đồng nghĩa