Gaussian curve - translation to ρωσικά
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  1. Λεξικά
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  3. Gaussian curve

Gaussian curve - translation to ρωσικά

MATHEMATICAL FUNCTION
Gaussian curve; Gaussian kernel; Gauss kernel; Error Curve; Error curve; Area under Gaussian curve; Area under the bell curve; Area under gaussian curve; Gauss curve; Integral of a Gaussian function; Integral of a Gaussian Function; Gauss bell
  • The [[discrete Gaussian kernel]] (solid), compared with the [[sampled Gaussian kernel]] (dashed) for scales <math>t = 0.5,1,2,4.</math>
  • 3d plot of a Gaussian function with a two-dimensional domain

Gaussian curve         
AMBIENT MUSIC GROUP
Gaussian Curve
гауссова /колоколообразная/ кривая
bell curve         
  • [[Carl Friedrich Gauss]] discovered the normal distribution in 1809 as a way to rationalize the [[method of least squares]].
  • As the number of discrete events increases, the function begins to resemble a normal distribution
  • Comparison of probability density functions, <math>p(k)</math> for the sum of <math>n</math> fair 6-sided dice to show their convergence to a normal distribution with increasing <math>na</math>, in accordance to the central limit theorem. In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve).
  • Histogram of sepal widths for ''Iris versicolor'' from Fisher's [[Iris flower data set]], with superimposed best-fitting normal distribution.
  • Fitted cumulative normal distribution to October rainfalls, see [[distribution fitting]]
  • [[Pierre-Simon Laplace]] proved the [[central limit theorem]] in 1810, consolidating the importance of the normal distribution in statistics.
  • The [[bean machine]], a device invented by [[Francis Galton]], can be called the first generator of normal random variables. This machine consists of a vertical board with interleaved rows of pins. Small balls are dropped from the top and then bounce randomly left or right as they hit the pins. The balls are collected into bins at the bottom and settle down into a pattern resembling the Gaussian curve.
  • '''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" />
  • The ground state of a [[quantum harmonic oscillator]] has the [[Gaussian distribution]].
  • For the normal distribution, the values less than one standard deviation away from the mean account for 68.27% of the set; while two standard deviations from the mean account for 95.45%; and three standard deviations account for 99.73%.
PROBABILITY DISTRIBUTION
Bell Curve; Gaussian distribution; NormalDistribution; Normal Distribution; Standard normal distribution; Law of error; Cumulative normal; Normally distributed; Cumulative Normal distribution; Normality (statistics); Standard normal; Normal density function; Normal curve; Normal distribution curve; Normal Curve; Normal random variable; The bell-shaped curve; Gaussian normal distribution; Gaussian Distributions; Gaussian Distribution; Bell-shaped; Gaussian random variable; Error Distribution; Bell-shaped curve; Standard distribution; Error distribution; Bell-curve; Normal distributions; Bell distribution; Normal probability distribution; Gaussian density; Gauss distribution; Normal cumulative distribution function; Bell Curves; Bell curves; Normal distribution about the mean; Gaussian probability density function; Gaussian probability distribution; Normal Model; Standard normal random variable; Gaussian profile; Normal-distribution; Bell-shaped frequency distribution curve; Gaussian distributions; Normal distribution quantile function; E-x2; E−x2; Normal population; Cumulative distribution function of the normal distribution; Bellcurve; Univariate Gaussian; Univariate Gaussian distribution; Bell curve; Bell shaped curve; Operations on normal deviates; Operations on normal distributions; Normal deviate; Standard normally distributed; Approximately normal distribution; Normalcdf; Gaussian pdf; Normal density; Normaldist

['belkə:v]

общая лексика

кривая нормального распределения

математика

колоколообразная

гауссова кривая

normally distributed         
  • [[Carl Friedrich Gauss]] discovered the normal distribution in 1809 as a way to rationalize the [[method of least squares]].
  • As the number of discrete events increases, the function begins to resemble a normal distribution
  • Comparison of probability density functions, <math>p(k)</math> for the sum of <math>n</math> fair 6-sided dice to show their convergence to a normal distribution with increasing <math>na</math>, in accordance to the central limit theorem. In the bottom-right graph, smoothed profiles of the previous graphs are rescaled, superimposed and compared with a normal distribution (black curve).
  • Histogram of sepal widths for ''Iris versicolor'' from Fisher's [[Iris flower data set]], with superimposed best-fitting normal distribution.
  • Fitted cumulative normal distribution to October rainfalls, see [[distribution fitting]]
  • [[Pierre-Simon Laplace]] proved the [[central limit theorem]] in 1810, consolidating the importance of the normal distribution in statistics.
  • The [[bean machine]], a device invented by [[Francis Galton]], can be called the first generator of normal random variables. This machine consists of a vertical board with interleaved rows of pins. Small balls are dropped from the top and then bounce randomly left or right as they hit the pins. The balls are collected into bins at the bottom and settle down into a pattern resembling the Gaussian curve.
  • '''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" />
  • The ground state of a [[quantum harmonic oscillator]] has the [[Gaussian distribution]].
  • For the normal distribution, the values less than one standard deviation away from the mean account for 68.27% of the set; while two standard deviations from the mean account for 95.45%; and three standard deviations account for 99.73%.
PROBABILITY DISTRIBUTION
Bell Curve; Gaussian distribution; NormalDistribution; Normal Distribution; Standard normal distribution; Law of error; Cumulative normal; Normally distributed; Cumulative Normal distribution; Normality (statistics); Standard normal; Normal density function; Normal curve; Normal distribution curve; Normal Curve; Normal random variable; The bell-shaped curve; Gaussian normal distribution; Gaussian Distributions; Gaussian Distribution; Bell-shaped; Gaussian random variable; Error Distribution; Bell-shaped curve; Standard distribution; Error distribution; Bell-curve; Normal distributions; Bell distribution; Normal probability distribution; Gaussian density; Gauss distribution; Normal cumulative distribution function; Bell Curves; Bell curves; Normal distribution about the mean; Gaussian probability density function; Gaussian probability distribution; Normal Model; Standard normal random variable; Gaussian profile; Normal-distribution; Bell-shaped frequency distribution curve; Gaussian distributions; Normal distribution quantile function; E-x2; E−x2; Normal population; Cumulative distribution function of the normal distribution; Bellcurve; Univariate Gaussian; Univariate Gaussian distribution; Bell curve; Bell shaped curve; Operations on normal deviates; Operations on normal distributions; Normal deviate; Standard normally distributed; Approximately normal distribution; Normalcdf; Gaussian pdf; Normal density; Normaldist

математика

нормально распределённый

распределённый по нормальному закону

с нормальным законом распределения

Βικιπαίδεια

Gaussian function

In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form

and with parametric extension for arbitrary real constants a, b and non-zero c. It is named after the mathematician Carl Friedrich Gauss. The graph of a Gaussian is a characteristic symmetric "bell curve" shape. The parameter a is the height of the curve's peak, b is the position of the center of the peak, and c (the standard deviation, sometimes called the Gaussian RMS width) controls the width of the "bell".

Gaussian functions are often used to represent the probability density function of a normally distributed random variable with expected value μ = b and variance σ2 = c2. In this case, the Gaussian is of the form

Gaussian functions are widely used in statistics to describe the normal distributions, in signal processing to define Gaussian filters, in image processing where two-dimensional Gaussians are used for Gaussian blurs, and in mathematics to solve heat equations and diffusion equations and to define the Weierstrass transform.

https://en.wikipedia.org/wiki/Gaussian function
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