Questions tagged [chi-distribution]

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

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Formulas or approximations for $\mathbb{E}\left( \frac{X}{\|X\|} \right)$, $X\sim N(\mu, Id)$?

This is a cross-posting of this math SE question. I want to compute or approximate the following expected value with some analytic expression: $\mathbb{E}\left( \frac{X}{||X||} \right)$ , where $X \in ...
dherrera's user avatar
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7 votes
1 answer
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Donut-like Distribution in Cartesian Coordinates

I have a set of points $P_i$ which are described by an angle $\theta_i$ and a magnitude $r_i$. $\theta_i$ follows a Uniform distribution $(\theta_i \sim U(0, 2\pi))$ and $r_i$ follows a chi-k ...
Liam F-A's user avatar
3 votes
1 answer
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Moments of inverse of a non-central chi distributed variable

I have a non-central chi variable $r$ with the distribution, \begin{align} p(r) = \frac{r^3\lambda}{(\lambda r)^{3/2}}\exp\left[-0.5(r^2 + \lambda^2)\right]I_{1/2}(r\lambda) \end{align} I'm looking ...
Nikhil Sharma's user avatar
1 vote
0 answers
74 views

Moments of a Ratio distribution (Normal variable / Non-central chi variable)

Let $[x_1, x_2, x_3]$ are three independent points in Cartesian space which are Gaussian distributed with a non-zero mean and identity covariance. I need to calculate the following expectations, \...
Nikhil Sharma's user avatar
3 votes
1 answer
98 views

Distribution of distances to mean of symmetric beta distribution

I have a symmetric beta distribution and draw d samples $x_i \sim Beta(a, a)$ for some a. Now I want to know the distribution of $\ell_2$-distances of the sample vector $(x_1, \dotsc, x_d)^T$ to the ...
Jannis's user avatar
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1 vote
0 answers
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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 ...
Paolo Cattaneo's user avatar
9 votes
1 answer
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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 ...
Denis Cousineau's user avatar
0 votes
1 answer
277 views

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's user avatar
2 votes
1 answer
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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....
Likk's user avatar
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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 $Y$? ...
D Satya Ganesh's user avatar
-1 votes
1 answer
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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.
Abhisekkkk's user avatar
3 votes
0 answers
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What it the distribution for square root of sum of squares of two independent normal distributed random variable? [closed]

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,\...
FantasticAI's user avatar
3 votes
2 answers
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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's user avatar
1 vote
1 answer
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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 ...
Arun's user avatar
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1 vote
0 answers
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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 ...
Jerome Swannack's user avatar
8 votes
3 answers
14k 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 ...
Delyle's user avatar
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8 votes
0 answers
985 views

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 ...
michalOut's user avatar
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4 votes
3 answers
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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 ...
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