# Questions tagged [non-central]

use for questions about socalled non-centrality parameters, in distributions such as t, F, chisquare, wishart and others.

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I have a problem where I want to find the distribution of the difference of two non-central chi squared random variables (RV), both independent. Given $$X=a+A\\ Y=b+B$$ where $a=a_r+ja_i$, $b=b_r+... 4 votes 1 answer 474 views ### ttest where the difference in the null hypothesis is not 0: non-centrality parameter? I have problems to understand when a non-centrality parameter is relevant. As far as I understood, if the t distribution is not centered on 0, a non-central t distribution is used. For example, in ... 3 votes 0 answers 147 views ### Distribution of the minimum of the squared Euclidean norm of a$N(\mu,\Sigma)$random variable Suppose that$X^n := \{x_1, x_2, \ldots, x_n\}$is a sample of$n$i.i.d$p$-dimensional points, where$X \sim N(\mu, \Sigma)$. What is known about the distribution of$\min_{x_i \in X^n} \|x_i\|^2_2$?... 0 votes 0 answers 279 views ### Sum of non-central chi-square using Laguerre expansion I moved this question from my answer on this link. From Castano-Martinez and Lopez-Blazquez(2005), They explained pdf of sum of noncentral Chi-square on equation 3.2, that is:$f(y)= \frac{e^{-\frac{...
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About non central chi-square, I have read paper from Castano-Martinez and Lopez-Blazquez(2005). They made expansion of $\chi_n^2(\delta)$ using inverse-Laplace transform and used Laguerre polynomial. ...
I'm writing functions (in R) that allow working with the $\omega^2$ distribution (the effect size for analysis of variance; the less biased alternative to $\eta^2$)....