Definitions for gaussian distribution
gauss·ian dis·tri·bu·tion

Princeton's WordNetRate this definition:0.0 / 0 votes

1. normal distribution, Gaussian distributionnoun

   a theoretical distribution with finite mean and variance

WiktionaryRate this definition:0.0 / 0 votes

1. Gaussian distributionnoun

   Normal distribution.

WikipediaRate this definition:0.0 / 0 votes

1. Gaussian Distribution

   In statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f ( x ) = 1 σ 2 π e − 1 2 ( x − μ σ ) 2 {\displaystyle f(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}} The parameter μ {\displaystyle \mu } is the mean or expectation of the distribution (and also its median and mode), while the parameter σ {\displaystyle \sigma } is its standard deviation. The variance of the distribution is σ 2 {\displaystyle \sigma ^{2}} . A random variable with a Gaussian distribution is said to be normally distributed, and is called a normal deviate. Normal distributions are important in statistics and are often used in the natural and social sciences to represent real-valued random variables whose distributions are not known. Their importance is partly due to the central limit theorem. It states that, under some conditions, the average of many samples (observations) of a random variable with finite mean and variance is itself a random variable—whose distribution converges to a normal distribution as the number of samples increases. Therefore, physical quantities that are expected to be the sum of many independent processes, such as measurement errors, often have distributions that are nearly normal.Moreover, Gaussian distributions have some unique properties that are valuable in analytic studies. For instance, any linear combination of a fixed collection of normal deviates is a normal deviate. Many results and methods, such as propagation of uncertainty and least squares parameter fitting, can be derived analytically in explicit form when the relevant variables are normally distributed. A normal distribution is sometimes informally called a bell curve. However, many other distributions are bell-shaped (such as the Cauchy, Student's t, and logistic distributions). For other names, see Naming. The univariate probability distribution is generalized for vectors in the multivariate normal distribution and for matrices in the matrix normal distribution.

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1. gaussian distribution

   A Gaussian distribution, also known as a normal distribution, is a type of continuous probability distribution for a real-valued random variable. It is characterized by its bell curve shape, where the mean, median, and mode of the distribution coincide. This distribution is symmetric around the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. The degree of the dispersion is defined by the standard deviation. Gaussian distributions are often used in the natural and social sciences to represent the distribution of random variables.

Matched Categories

1. • Distribution
   • Statistics

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Numerology

1. Chaldean Numerology

   The numerical value of gaussian distribution in Chaldean Numerology is: 9

2. Pythagorean Numerology

   The numerical value of gaussian distribution in Pythagorean Numerology is: 8

References

1. ^ Princeton's WordNet
   http://wordnetweb.princeton.edu/perl/webwn?s=gaussian distribution
2. ^ Wiktionary
   https://en.wiktionary.org/wiki/Gaussian_Distribution
3. ^ Wikipedia
   https://en.wikipedia.org/wiki/Gaussian_Distribution
4. ^ ChatGPT
   https://chat.openai.com