# Questions tagged [absolute-value]

Question concerns the consequences of using the absolute value function in part of the definition of one or more statistics.

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### Need help understanding how only variable A can be correlated to the absolute value of A-B

I'm currently working with the dataset of a study I'm conducting. The data is comprised of serially drawn samples from patients where we've measured the cell counts of those samples and compared them ...
56 views

### An interesting non-smooth regression

Consider the following setup: Let $x_1^k$ and $x_2^k$ be length $N$ vectors of observed reals, where $N$ is about, say, 100,000, $k\in 1:K$, and $K$ is about, say, 200. (So $x_1,\;x_2$ can be thought ...
159 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 ...
176 views

### Expected value of the absolute standardized t distribution

What is the expected value of the absolute standardized t-distribution - i.e.,: $E(|X|)$, where $X$ has the standardized t-distribution?
165 views

### Compounding a Gaussian distribution with variance distributed according to the absolute value of another Gaussian distribution

Have there been earlier descriptions of the following compound distribution? Compounding a Gaussian distribution with variance distributed according to the absolute value or square of another ...
27 views

### Why is there a need to find a variance and take the square root to get a standard deviation? [duplicate]

My question is why is the formula for finding the standard deviation of a given data (either grouped or non grouped) the way it is? so let me start from the definition of a standard deviation with my ...
799 views

### What is the expectation of the absolute value of the Skellam distribution?

In particular, for a Skellam distribution obtained by substracting two iid Poisson Processes. Thank you!
2k views

### Why should I prefer the standard deviation over other measures of variance? [duplicate]

The most common kind of deviation is the standard deviation. $$\text{Sd}(x) = \sqrt{\text{Mean}((x - \text{Mean}(x))^2)}$$ The standard deviation is very similar to the mean absolute deviance or ...