Questions tagged [absolute-value]
Question concerns the consequences of using the absolute value function in part of the definition of one or more statistics.
10
questions
5
votes
2answers
52 views
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 ...
1
vote
0answers
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 ...
5
votes
1answer
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 ...
8
votes
1answer
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?
3
votes
1answer
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 ...
1
vote
0answers
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 ...
6
votes
1answer
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!
2
votes
3answers
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
$$...
6
votes
2answers
1k views
Is the absolute value of the difference between two Poisson distributions a Poisson distribution?
What is the distribution of the absolute value of the Skellam distribution?
462
votes
22answers
234k views
Why square the difference instead of taking the absolute value in standard deviation?
In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute ...
