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Normal distribution
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== See also == {{Portal|Mathematics}} * [[Bates distribution]] – similar to the Irwin–Hall distribution, but rescaled back into the 0 to 1 range * [[Behrens–Fisher problem]] – the long-standing problem of testing whether two normal samples with different variances have same means; * [[Bhattacharyya distance]] – method used to separate mixtures of normal distributions * [[Erdős–Kac theorem]] – on the occurrence of the normal distribution in [[number theory]] * [[Full width at half maximum]] * [[Gaussian blur]] – [[convolution]], which uses the normal distribution as a kernel * [[Gaussian function]] * [[Modified half-normal distribution]]<ref name="Sun-2021">{{cite journal |last1=Sun |first1=Jingchao |last2=Kong |first2=Maiying |last3=Pal |first3=Subhadip |title=The Modified-Half-Normal distribution: Properties and an efficient sampling scheme |journal=Communications in Statistics – Theory and Methods |date=22 June 2021 |volume=52 |issue=5 |pages=1591–1613 |doi=10.1080/03610926.2021.1934700 |s2cid=237919587 |url=https://www.tandfonline.com/doi/abs/10.1080/03610926.2021.1934700?journalCode=lsta20 |issn=0361-0926}}</ref> with the pdf on <math display=inline>(0, \infty)</math> is given as <math display=inline>f(x)= \frac{2\beta^{\frac{\alpha}{2}} x^{\alpha-1} \exp(-\beta x^2+ \gamma x )}{\Psi{\left(\frac{\alpha}{2}, \frac{ \gamma}{\sqrt{\beta}}\right)}}</math>, where <math display=inline>\Psi(\alpha,z)={}_1\Psi_1\left(\begin{matrix}\left(\alpha,\frac{1}{2}\right)\\(1,0)\end{matrix};z \right)</math> denotes the [[Fox–Wright Psi function]]. * [[Normally distributed and uncorrelated does not imply independent]] * [[Ratio normal distribution]] * [[Reciprocal normal distribution]] * [[Standard normal table]] * [[Stein's lemma]] * [[Sub-Gaussian distribution]] * [[Sum of normally distributed random variables]] * [[Tweedie distribution]] – The normal distribution is a member of the family of Tweedie [[exponential dispersion model]]s. * [[Wrapped normal distribution]] – the Normal distribution applied to a circular domain * [[Z-test]] – using the normal distribution
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