# Questions tagged [chi-distribution]

The chi-distribution is the square root of a chi-square distribution.

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### The square root of weighted sum of chi-squared distribution

Let $X\sim\chi_m^2$ and $Y\sim\chi_n^2$ be two independent variables. How to calculate or estimate the expectation of $\sqrt{aX+bY}$, where $a,b>0$?
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### Generating Priors on Lambda for a non-central Chi Distribution of Euclidean Norm of a vector based on component normally distributed elements

I am trying to calculate a posterior predictive distribution for the magnitude (Euclidean norm) of a 3D displacement vector. Displacement in each dimension is independent and normally distributed (but ...
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### Finding the probability of a Nearest Neighbour miss-identification in 8 dimensions

I'm trying to ascertain the accuracy of a device used to distinguish values from different populations. Currently each device measurement contains a data point from 8 different sensors. The value ...
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### How to Estimate Population Variance from Multiple Samples

Suppose I have $N$ samples each of size $n$, drawn from the same population, where each sample has its own sample variance $s_i^2$. I understand that for any given sample, a first estimate of the ...
Assume $M$ is an $N \times k$ Gaussian matrix, i.e., its entries are i.i.d. standard normal random variables, with $N>>k$. Take $D=\text{diag}(\lambda_1, \dotsc ,\lambda_N)$ for some fixed real ...