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What (who) is normal distribution - definition

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

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

normal distribution

¦ noun Statistics a function that represents the distribution of many random variables as a symmetrical bell-shaped graph.

normal distribution

<statistics> (Or "Gaussian distribution") The {frequency distribution} of many natural phenomena such as the height or intelligence of people of a certain age and sex. The formula looks something like: P(x) = e^(((x-m)/s)^2) where P(x) is the probability of a measurement x, m is the mean value of x and s is the standard deviation. Also known as a "bell curve" because of its shape. (2003-10-25)

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

Examples of use of normal distribution

1. Low–level officials do not grasp that hundreds of polling stations reporting figures in round numbers distort normal distribution, thus clearly revealing manipulations, Delyagin said.

2. He said it did not have the normal distribution of prions, the misfolded mad cow proteins that kill brain cells and leave spongy holes behind.

3. "That is within the normal distribution." In total, the company has 75 alliances, ranging from control at Genentech to minority participations and licensing agreements in small biotech businesses.

4. After that, it begins spiking on round numbers, indicating a much greater number of polling stations reporting a specific turnout than a normal distribution would predict.

5. A 30–year–old mother of two, Kadem is part of a novel Hindustan Lever initiative that enlists about 20,000 poor and mostly illiterate women to peddle such products as Lifebuoy soap and Pepsodent toothpaste in villages once considered too small, too destitute and too far from normal distribution channels to warrant attention.