# 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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### G*Power: Sensitivity Z-test, Compute non centrality parameter given alpha and power

I am using the Z test: Generic Z test, sensitivity tool. I have a distribution of values of the normal population sample with a mean and SD so I thought the non centrality parameter would give me the ...
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### How do I get the alpha and beta of a non-central beta distribution from mean and variance in R?

I need to fit a beta-distribution a real data, with a mean of 0 and a standard deviation of 0.17. I have read that this is possible by using the non-central beta distribution, and I would wlike to ...
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### A question concerning distribution of $\mathbf{Y}/\|\mathbf{Y}\|_2$ where $\mathbf{Y}\sim \mathcal{N}(\boldsymbol{\mu},\mathbf{I})$

I know that when $\mathbf{Y}\sim\mathcal{N}(\mathbf{0},\mathbf{I})$, $\mathbf{Y}/\|\mathbf{Y}\|_2$ is distributed uniformly on the unit sphere. But to my surprise, I failed to find a simple closed ...
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### How to calculate non centrality parameter?

Suppose $Y\sim N_p(\mu,\sigma^2I_p)$. Let $A$ be a symmetric idempotent matrix. I want to show $Y^{T}AY$ follows a chi-sq distribution with some non centrality parameter. Suppose $tr(A)=r(A)=k$. ...
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### Is there a PDF for a generalized non-central chi-squared distribution [duplicate]

Is there a PDF for a distribution defined as a sum of squares of random variables pulled from a family of normal distributions with different standard deviation? Is there a way of analytically ...
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### Noncentrality Parameter - what is it, what does it do, what would be a suggested value?

I have been trying to brush up on my stats knowledge, especially in relation to Sample size determination and Statistical Power Analysis. But it seems that the more I read the more I need to read. ...
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### Is there a known generalization of the doubly noncentral t-distribution?

Given $p$-variate normal $X \sim \mathcal{N}\left(\mu,\Sigma\right)$, consider the random variable $$t_* = \frac{X_1}{\sqrt{\sum_{2\le i \le p} X_i^2}}.$$ For some values of $\Sigma$, this ...
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### Generate data from a t-distribution with specified mean and standard deviation [duplicate]

How does one randomly sample from a T-distribution in R. From what I've found, the function rt in R doesn't let you specify the mean and standard deviation. For a ...
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### Efficient fitting of noncentral chi-squared distribution to data?

I am looking for the most efficient way to fit a noncentral chi-squared distribution with fixed d.o.f. to a given data set. So the inputs are d.o.f. and the data and the output should be the ...
Suppose that you observe $F_1,F_2,\ldots,F_k$ each independently. drawn from non-central F distributions with common, known, d.f. $\nu_1, \nu_2$, and with (unknown) non-centrality parameters $\... 0answers 377 views ### Distribution of a normalized inverse Wishart times Gaussian Suppose$z\sim\mathcal{N}\left(\lambda^2 e_1,I_n\right)$where$e_1$is the first column of the$n$-dimensional identity matrix, denoted here as$I_n$. Suppose$S\sim\mathcal{W}\left(m,I_n\right)$is ... 0answers 167 views ### What is the distribution of the 'achieved'$R^2$? I am interested in the distribution of/performing inference on the 'achieved'$R^2$coefficient in multiple linear regression. Suppose that$y\sim x\beta + \epsilon$with$\epsilon \sim \mathcal{N}\...
I am wondering if there are standard naming conventions in general for confidence distributions or for the particular cases of the non-centrality parameters of (non-central) $t$- and $F$-distributions....