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Questions tagged [non-central]

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

4
votes
1answer
365 views

Why are these two random variables identically distributed?

Let $(X_1, X_2, \ldots, X_i, \ldots, X_k)$ be $k$ independent, normally distributed random variables with means $\mu_i$ and variances $1$. Then the random variable $$ \sum_{i=1}^k X_i^2$$ is ...
11
votes
2answers
2k views

What is the power of the regression F test?

The classical F-test for subsets of variables in multilinear regression has the form $$ F = \frac{(\mbox{SSE}(R) - \mbox{SSE}(B))/(df_R - df_B)}{\mbox{SSE}(B)/df_B}, $$ where $\mbox{SSE}(R)$ is the ...
8
votes
5answers
543 views

Confidence Interval on a random quantity?

Suppose $\vec{a}$ is an unknown $p$-vector, and one observes $\vec{b} \sim \mathcal{N}\left(\vec{a}, I\right)$. I would like to compute confidence intervals on the random quantity $\vec{b}^{\top} \...
7
votes
1answer
6k views

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. ...
3
votes
1answer
191 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 ...
2
votes
1answer
86 views

Which distribution do I get?

Be $X\sim N(\mu,1)$ and $Y\sim Inverse-Gamma(\alpha,\beta)$. For the Inverse-Gamma, I usually use the parameterization which leads to the following probability distribution function for Y: $f(y;\...
2
votes
1answer
687 views

Relationship between the gamma distribution and Non-central chi squared distribution?

If $Y = \sum_{i=1}^N X_i^2 $, where $X_i \sim \mathcal{N}(\mu,\sigma^2)$, i.e. all $X_i$ are i.i.d gaussian random variables of same mean and variance, then what is the resultant PDF of $Y$? How the ...
2
votes
0answers
702 views

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 ...