# Questions tagged [chi-distribution]

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

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### What is the distribution of the difference between two random numbers?

I have a big bag of balls, each one marked with a number between 0 and $n$. The same number may appear on more than one ball. We can assume that the numbers on the balls follow a binomial distribution....
161 views

### How to calculate mean and variance of non central chi distribution of the problem?

If $Y = \sqrt{\sum_{i=1}^N X_i^2}$, 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 $Y$? ...
86 views

### Which distribution is this [closed]

I know this will be a f distribution.But it's not f(m,n) since the square sign is outside the summation.So it will be f(1,n).But i can't seem to know how exactly.
436 views

### 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 $a,b>0$?
70 views

### 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 ...
26 views

### 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 ...
5k views

### 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 $N \times k$ Gassian 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 ...