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Chi-squared distribution
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== See also == {{Portal|Mathematics}} {{Colbegin}} * [[Chi distribution]] * [[Scaled inverse chi-squared distribution]] * [[Gamma distribution]] * [[Generalized chi-squared distribution]] * [[Noncentral chi-squared distribution]] * [[Pearson's chi-squared test]] * [[Reduced chi-squared statistic]] * [[Wilks's lambda distribution]] * [[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://figshare.com/articles/journal_contribution/The_Modified-Half-Normal_distribution_Properties_and_an_efficient_sampling_scheme/14825266/1/files/28535884.pdf |issn=0361-0926}}</ref> with the pdf on <math>(0, \infty)</math> is given as <math> f(x)= \frac{2\beta^{\alpha/2} x^{\alpha-1} \exp(-\beta x^2+ \gamma x )}{\Psi{\left(\frac{\alpha}{2}, \frac{ \gamma}{\sqrt{\beta}}\right)}}</math>, where <math>\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]]. {{Colend}}
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