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The following 13 pages use this file: Bell-shaped function; Gaussian function; Information geometry; Normal distribution; Probability distribution fitting; User:Jlee4203/sandbox; User:Minzastro/sandbox; User:OneThousandTwentyFour/sandbox; Wikipedia:Top 25 Report/September 16 to 22, 2018; Template:Infobox probability distribution
The simplest case of a normal distribution is known as the standard normal distribution or unit normal distribution. This is a special case when μ = 0 {\textstyle \mu =0} and σ 2 = 1 {\textstyle \sigma ^{2}=1} , and it is described by this probability density function (or density): φ ( z ) = e − z 2 2 2 π . {\displaystyle \varphi (z ...
In probability and statistics, the truncated normal distribution is the probability distribution derived from that of a normally distributed random variable by bounding the random variable from either below or above (or both). The truncated normal distribution has wide applications in statistics and econometrics.
The fact that two random variables and both have a normal distribution does not imply that the pair (,) has a joint normal distribution. A simple example is one in which X has a normal distribution with expected value 0 and variance 1, and = if | | > and = if | | <, where >. There are similar counterexamples for more than two random variables.
The probability density function for the random matrix X (n × p) that follows the matrix normal distribution , (,,) has the form: (,,) = ([() ()]) / | | / | | /where denotes trace and M is n × p, U is n × n and V is p × p, and the density is understood as the probability density function with respect to the standard Lebesgue measure in , i.e.: the measure corresponding to integration ...
In statistics, the Q-function is the tail distribution function of the standard normal distribution. [ 1 ] [ 2 ] In other words, Q ( x ) {\displaystyle Q(x)} is the probability that a normal (Gaussian) random variable will obtain a value larger than x {\displaystyle x} standard deviations.
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The folded normal distribution is a probability distribution related to the normal distribution. Given a normally distributed random variable X with mean μ and variance σ 2, the random variable Y = |X| has a folded normal distribution. Such a case may be encountered if only the magnitude of some variable is recorded, but not its sign.