Questions tagged [non-central]

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

8 questions
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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 ...
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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 ...
548 views

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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 ...
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 ...