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Wat (wie) is Gaussian distribution - definitie

PROBABILITY DISTRIBUTION

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$'''a:''' Probability density of a function <math>\cos x^2</math> of a normal variable <math>x</math> with <math>\mu=-2</math> and <math>\sigma=3</math>. '''b:''' Probability density of a function <math>x^y</math> of two normal variables <math>x</math> and <math>y</math>, where <math>\mu_x=1</math>, <math>\mu_y=2</math>, <math>\sigma_x = 0.1</math>, <math>\sigma_y = 0.2</math>, and <math>\rho_{xy} = 0.8</math>. '''c:''' Heat map of the joint probability density of two functions of two correlated normal variables <math>x</math> and <math>y</math>, where <math>\mu_x = -2</math>, <math>\mu_y=5</math>, <math>\sigma_x^2 = 10</math>, <math>\sigma_y^2 = 20</math>, and <math>\rho_{xy} = 0.495</math>. '''d:''' Probability density of a function <math display="inline">\sum_{i=1}^4 \vert x_i \vert</math> of 4 iid standard normal variables. These are computed by the numerical method of ray-tracing.<ref name="Das" />$

Gaussian distribution

['ga?s??n]

¦ noun Statistics another term for normal distribution.

Gaussian distribution

normal distribution

Bell-shaped

·adj Having the shape of a wide-mouthed bell; campanulate.

Wikipedia

Normal 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)={\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}

The parameter $\mu$ is the mean or expectation of the distribution (and also its median and mode), while the parameter $\sigma$ is its standard deviation. The variance of the distribution is $\sigma ^{2}$ . 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.

https://en.wikipedia.org/wiki/Normal distribution

Voorbeelden uit tekstcorpus voor Gaussian distribution

1. In most elections, one would expect the turnout to follow a normal, or Gaussian, distribution –– meaning that a chart of the number of polling stations reporting a certain turnout would be shaped like a bell curve, with the top of the bell representing the average, median, and most popular value.