Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [chi-distribution]

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

The chi-distribution is the square root of a chi-square distribution. That is, it arises as the square root of a sum of squares of independent standard normal random variables. It has a degrees of freedom parameter, as with the chi-square.

The absolute value of a standard normal is an example of a chi-distribution (it has a chi(1) distribution), as is the Rayleigh(1) distribution (chi(2)) and the Maxwell distribution (normalized molecular speeds, which are chi(3)).

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Distribution of the pooled variance in paired samples

Suppose a bivariate normal populations with means $\mu_1$ and $\mu_2$ and equal variance $\sigma^2$ but having a correlation of $\rho$. Taking a paired sample, it is possible to compute the pooled variance. If $S^2_1$ and $S^2_2$ are the sample…
Denis Cousineau
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QR decomposition of normally distributed matrices

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 scalars. I am interested in finding the p.d.f. of the…
michalOut
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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 population variance $\sigma^2$ is: $$\hat{\sigma}^2…
Delyle
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Efficient generation of chi random variables

I need to generate random variables generated from a chi distribution (not chi-squared!). There doesn't seem to be standard mechanism in C++ in (for example) Boost::Random and hence I am looking for an alternative implementation implemented in C++…
Damien
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What it the distribution for square root of sum of squares of two independent normal distributed random variable?

What it the distribution for square root of sum of squares of two independent normal distributed random variable? Assuming they have zero mean and same non-zero variance. Suppose $X$ and $Y$ ~ $N(0,\sigma^2)$, what is the distribution for $Z =…
FantasticAI
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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. Now I pick a random ball from the bag, read its…
Likk
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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 $a,b>0$?
user07001129
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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 each may have different means and variances).…
Arun
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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 recorded from this sensor approximately belonging to…
Jerome Swannack
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Expected distance between (X, Y), where both X and Y are standrd normal random variabls and the origin

Let $(X, Y)$ be two independent standard random variable, with mean and SD being 0 and 1 respectively. What would be $E[\sqrt(X^2 + Y^2)]$, the expected distance between $(X, Y)$ and the origin.
kangtinglee
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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 $Y$? How to calculate the mean and variance of the…
D Satya Ganesh
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Which distribution is this

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.
Abhisekkkk
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