# Questions tagged [chi-squared-distribution]

The distribution of sum-of-squares of k independent standard normal random variables. For the test, use the [chi-squared-test] tag. Use also for related distributions.

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### Scalar product of Gaussian random vector with projection matrix is chi-squared

We define the $n$ chi-square random variable this way : if $Z \sim N(0,I_n)$ is multivariate Gaussian random vector, then $\lVert Z \rVert ^2 = \sum_{i=1}^n Z_i^2$ (sum of $n$ standard gaussian RV ...
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### Degrees of freedom of Sample Variance of Residuals (Chi-Square distribution?

In the context of jointly testing J linear restrictions, I am reviewing the distribution of the F-statistic, which is F(J, n-k). Below, R is a full row rank Jxk matrix, q is a Jx1 vector, and the null ...
1 vote
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### Distribution of exponent of multivariate normal distribution

My slides say that the exponent of a multivariate normal distribution, $(\mathbf{X} - \boldsymbol{\mu})^\text{T} \boldsymbol{\Sigma}^{-1} (\mathbf{X} - \boldsymbol{\mu})$, follows a chi squared ...
1 vote
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### What are the relevant null distributions to infer the results of a simulation that renders a multinomial distribution with three possible results?

I have simulated 10 000 occurrences of a soccer match, by generating random numbers from 0 to 1, and then passing these, and the adjusted expected goals by team for the match, through an inverse ...
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1 vote
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### Detecting multivariate outliers with Minimum covariance discriminant and mahalanobis distance

I've read in some papers (such as this) and CrossValidated questions (such as this, that people are using mahalanobis distance based on robust estimations of location and scatter using minimum ...
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### limit of $\frac{\lambda}{\chi _{2Y}^{2}}$ as $Y \sim Poisson(n\lambda)$ and $𝜆 → ∞$

There are the following lines in Casella & Berger on page 438, before the equation (9.2.22): ..., write $$\lambda = \frac{\lambda}{\chi _{2Y}^{2}}\chi _{2Y}^{2}$$ where $\chi _{2Y}^{2}$ is a chi ...
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1 vote
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### How can I find the standard deviation of the sample standard deviation from N normal distribution?

I'm an energy engineer, so my knowledge on the argument is rather limited, so forgive me in case it's a stupid question. This question is very linked to this: How can I find the standard deviation of ...
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### Understanding the relationship between the scaled inverse $\chi^2$ and inverse $\chi^2$ distributions

wikipedia says that Also, the scaled inverse chi-squared distribution is presented as the distribution for the inverse of the mean of ν squared deviates, rather than the inverse of their sum. The two ...
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