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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 ...
If X is a gamma(α, β) random variable and the shape parameter α is large relative to the scale parameter β, then X approximately has a normal random variable with the same mean and variance. If X is a Student's t random variable with a large number of degrees of freedom ν then X approximately has a standard normal distribution.
English: A selection of Normal Distribution Probability Density Functions (PDFs). Both the mean, μ , and variance, σ² , are varied. The key is given on the graph.
Skew normal distribution; Skewed generalized t distribution; Slash distribution; Split normal distribution; Standard normal deviate; Standard normal table; Student's t-distribution; Sum of normally distributed random variables
In directional statistics, the projected normal distribution (also known as offset normal distribution, angular normal distribution or angular Gaussian distribution) [1] [2] is a probability distribution over directions that describes the radial projection of a random variable with n-variate normal distribution over the unit (n-1)-sphere.
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The equidensity contours of a non-singular multivariate normal distribution are ellipsoids (i.e. affine transformations of hyperspheres) centered at the mean. [29] Hence the multivariate normal distribution is an example of the class of elliptical distributions.
In this context, the log-normal distribution has shown a good performance in two main use cases: (1) predicting the proportion of time traffic will exceed a given level (for service level agreement or link capacity estimation) i.e. link dimensioning based on bandwidth provisioning and (2) predicting 95th percentile pricing. [94]