Questions tagged [absolute-value]

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

Filter by
Sorted by
Tagged with
0 votes
0 answers
34 views

Analogous result to Isserlis' theorem for mixed absolute product-moments of multivariate normal distribution

Suppose that $(X_1, \cdots, X_n)$ have a joint normal distribution. If $n = 2m + 1$, then $\mathbb{E} \left[ \prod_{j=1}^n X_j \right] = 0$. This can be argued from the symmetry of the multivariate ...
user avatar
  • 3,696
0 votes
1 answer
32 views

Solve an inequality finding the upper bound

Suppose that there exists a constant $C$ such that the following relation holds for all $G$: \begin{equation*} \vert T(F)-T(G) \vert \le C \sup_y \vert F(y)-G(y) \vert \end{equation*} Suppose that ...
user avatar
  • 57
0 votes
0 answers
41 views

Test which time series is closer to zero

I have two time series, A and B, which represent reactions of subject A and B to a certain medication measured at different point in times. I want to formally test that the reaction of patient A is ...
user avatar
  • 46
0 votes
0 answers
26 views

Absolute of expected value of multivariate correlated Bernoulli

I am running some experiment where I draw samples from a multivariate Bernoulli distribution (in this case taking values -1 or +1) with a single correlation coefficient (i.e., same correlation for all ...
user avatar
0 votes
0 answers
39 views

Computing Expected Values for Skewed generalized $t$ distribution

If $X$ has a Skewed generalized t distribution , whose PDF is given by $$f\left(x;\mu,\sigma,\lambda,p,q\right)=\frac{p}{2\nu\sigma q^{1/p}B\left(1/p,q\right)\left(\frac{\vert x-\mu+m\vert}{q\left(\...
user avatar
0 votes
1 answer
90 views

MGF of the absolute Value of a Skellam RV

I am trying to derive the moment generating function for the absolute value of a Skellam random variable $Skellam(\lambda_1, \lambda_2)$ Suppose $X_1 \sim Pois(\lambda_1)$ and $X_2 \sim Pois(\lambda_2)...
user avatar
  • 520
4 votes
1 answer
66 views

Finding the value of $k$ for an Uniform Distribution defined on $(-k,k)$

If $X$ be an uniform distribution defined on $(-k,k)$, then the value of $k$ for so that : $$P(|X|<1) = P(|X|>2)$$ I began by defining the $p.d.f$ of the Uniform function namely: $$ f(x) = \...
user avatar
  • 423
1 vote
0 answers
127 views

Expectation of absolute random variable and its relationship with absolute expectation value

For any continuous random variable $X$, it is obvious that $|E X| \leq E|X|$. My question is, what kind of distribution $P$, such that $X\sim P$ and satisfy $|E X| \geq c E|X|$ for some positive $c\in ...
user avatar
4 votes
3 answers
111 views

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 ...
user avatar
  • 71
5 votes
2 answers
92 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 ...
user avatar
2 votes
0 answers
70 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 ...
user avatar
6 votes
1 answer
755 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 ...
user avatar
8 votes
1 answer
666 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?
user avatar
3 votes
1 answer
350 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 ...
user avatar
1 vote
0 answers
28 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 ...
user avatar
  • 121
6 votes
1 answer
997 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!
user avatar
2 votes
3 answers
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 $$...
user avatar
6 votes
2 answers
2k 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?
user avatar
  • 63
530 votes
23 answers
285k 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 ...
user avatar
  • 5,545