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In probability theory and statistics, the Rayleigh distribution is a continuous probability distribution for nonnegative-valued random variables.Up to rescaling, it coincides with the chi distribution with two degrees of freedom.
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If Y has a half-normal distribution, then (Y/σ) 2 has a chi square distribution with 1 degree of freedom, i.e. Y/σ has a chi distribution with 1 degree of freedom. The half-normal distribution is a special case of the generalized gamma distribution with d = 1, p = 2, a = 2 σ {\displaystyle {\sqrt {2}}\sigma } .
In the empirical sciences, the so-called three-sigma rule of thumb (or 3 σ rule) expresses a conventional heuristic that nearly all values are taken to lie within three standard deviations of the mean, and thus it is empirically useful to treat 99.7% probability as near certainty.
When μ = 0, the distribution of Y is a half-normal distribution.; The random variable (Y/σ) 2 has a noncentral chi-squared distribution with 1 degree of freedom and noncentrality equal to (μ/σ) 2.
Run chart illustrating the 1.5 sigma drift Six Sigma concept File usage No pages on the English Wikipedia use this file (pages on other projects are not listed).
In quantum field theory, a nonlinear σ model describes a field Σ that takes on values in a nonlinear manifold called the target manifold T.The non-linear σ-model was introduced by Gell-Mann & Lévy (1960, §6), who named it after a field corresponding to a spinless meson called σ in their model. [1]
The Nakagami distribution or the Nakagami-m distribution is a probability distribution related to the gamma distribution.The family of Nakagami distributions has two parameters: a shape parameter / and a scale parameter >.