Questions tagged [folded-normal-distribution]

The distribution of the absolute value of a normally distributed variable.

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3answers
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Distribution of errors

I am struggeling with a basic question and would be happy to get some pointers. I am trying to evaluate an algorithm $f$ which maps some sample $x$ onto a scalar $y\in\mathbb{R}$, i.e. $f(x) = y$. For ...
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0answers
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Folded Normal Distribution Shape Parameter?

Scipy, a python library, says the pdf of a folded normal distribution is as shown here: http://pageperso.lif.univ-mrs.fr/~francois.denis/IAAM1/scipy-html-1.0.0/tutorial/stats/continuous_foldnorm.html ...
1
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1answer
87 views

How do you calculate the expected value of $E\left\{e^{-|X|}\right\}$ e.g. for Gaussian X?

If $X$ is a random variable, I would like to be able to calculate something like $$E\left\{e^{-|X|}\right\}$$ How can I do this, e.g., for a normally distributed $X$?
6
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1answer
365 views

Expectation of sum of absolute values for correlated normal random variables

Let $x_1, x_2, \dots, x_{N}$ i.i.d. random variables $\sim \mathcal{N}\left(0,\sigma^2_x\right)$. Further, let $z\sim \mathcal{N}\left(0,\sigma^2_z\right)$, $z$ is independent from all $x_i$. We build ...
4
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1answer
42 views

Unbiased estimator when only the magnitude can be measured

given an random variable $x$, which is drawn from a normal distribution $f(x| \mu_x, \sigma_x) = \frac{1}{\sqrt{2 \pi \sigma_x^2}} \exp\left(-\frac{(x-\mu_x)^2}{2 \sigma_x^2}\right)$. We are drawing $...
3
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1answer
581 views

Confidence interval for a folded normal distribution

(My background: physicist rusty on statistics, evaluating an experimental dataset). I'm studying a dataset with a random variable $X$, which is approximately normally distributed with standard ...
0
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1answer
238 views

First order statistic of folded normal

Are there any good approximations or tail bounds for the first-order statistic of the folded normal, or the closely related chi-square distribution with $k$ degrees of freedom? It seems that the $n$-...
8
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2answers
2k views

Is the variance of the multivariate folded normal distribution known?

The mean and variance of the folded normal distribution are known. Consider now the distribution of $(|x_1|, \ldots, |x_n|)$, where $\mathbb{x} \sim N(\mu, \Sigma)$. The mean of the multivariate ...