For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].

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2
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1answer
41 views

help understanding step in derivation of correlation coefficient

I'm looking to understand the starred step in the derivation below (also, if someone could help with the LaTex alignment, I'd appreciate it). The regression line is $y= b_0 + b_1 x$, where $b_0$ and ...
0
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0answers
32 views

Correlation function of Brownian motion. What am I doing wrong?

Can anyone tell me where I am going wrong here? (I am leaving out any random fluctuation forcings, because I don't think they are relevant to my problem.) 1: $\displaystyle \frac{dv(t)}{dt}=-\eta ...
0
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0answers
13 views

What is a correct way to calculate the correlation of a phase?

To do a correlation or an autocorrelation of a magnitude or a complex number is straightforward. But what if you want to calculate the correlation of a phase? The problem being that, if your phases ...
1
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0answers
34 views

Calculation of conditional joint probability given certain conditionals for data which aren't independent

The context of this problem is the estimation of the distribution of a parameter $v$ given sets of data $A$ and $B$, where $A$ and $B$ are not independent. Suppose I know $P(v | A)$ and $P(v | B)$. ...
0
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0answers
14 views

Calculating mean of data given correlated data pairs (how to apply Bayes theorem)?

Suppose that I have a data set of points $\{A_i\}$ and $\{B_i\}$. These data points are not independent, and the pairing is A1 <--> B1, A2 <--> B2 etc (i.e. the points come in pairs). I want to ...
0
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0answers
14 views

Rebuild functions from Matrix(or any form) of unknown functions output

if I have a matrix that represent the output of several distinct functions, the output of every function is connected on the matrix (e.g.a11,a12 OR a11,a21-but not a11,a13) -is there a way to ...
1
vote
1answer
48 views

correlation of product with its normally distributed factors

If x and y are normally dist. with standard deviation of 10%, and they are independent, then their product X.Y is 71% correlated with Y (or X). I can show this empirically, but how to I prove it in ...
0
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2answers
47 views

Trying to understand correlation and independence geometrically

I am trying to understand correlation and independence of two random variables geometrically, but found it difficult to grasp the intuition and to explain it rigorously. First, given two uniformly ...
2
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0answers
50 views

Dimension free Concentration bounds for Martingales

Consider the following random process which is defined on $n$ numbers $0\leq x_1,\ldots,x_n\leq 1$: At each step, pick an arbitrary number, say $x_i$. Then randomly (and independently) change its ...
0
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0answers
21 views

Calculate the tendency of a set of samples [migrated]

I develop an application in which I constantly get samples of heart pulse. I defined an interval of $t$ seconds. In each $t$ seconds I have $n$ samples. In every interval, I want to calculate the ...
2
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0answers
18 views

Finding the empirical correlation from a covariance matrix

I have this covariance matrix with five variables $X_1$ through $X_5$ in that order. ...
0
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0answers
21 views

Correlation question

I hope someone can help me with this: Let $c(\rho)=\lim_{n\rightarrow\infty}n^{\alpha-1}\sum_{k=-(n-1)}^{n-1}\left[1-\frac{k}{n}\rho(k)\right]$ where $n=1,2,3,\ldots$, $\alpha\in(0,1)$ and $\rho$ is ...
1
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1answer
36 views

Random walk serial correlation

Given a model $$Y_t =b_0 + b_1 \cdot X_t + b_2 \cdot Z_t + e_t,$$ where the error term $e_t$ follows a random walk form of serial correlation $e_t = e_{t-1} + u_t$. Further assume $u_t$ has zero mean ...
1
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1answer
52 views

Inequality concerning the pairwise correlation coefficients of three random variables

I was asked to prove: The correlation coefficients, $\rho_{12}$, $\rho_{23}$, $\rho_{13}$ between three random variables $X_1$, $X_2$, $X_3$ obey ...
0
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1answer
96 views

Covariance and Correlation

Suppose there were m married couples, but d of these 2m people have died. Regard the d deaths as striking the 2m people at random. Let X be the number of surviving couples. Find: a) E(X) b) Var(X) ...
0
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1answer
41 views

Correlation of Indicator Variables

Show that for indicator random variables IA and IB of Events A and B: Corr(IA, IB) = Corr(IAc, IBc) = -Corr(IA, IBc) = -Corr(IAc, IB) Deduce that if A and B are positively dependent, then so are Ac ...
0
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0answers
43 views

Invariance of the correlation coefficient under linear transformations

Show that for arbitrary random variables X and Y, and constants a ,b ,c ,d with a and c nonzero, Corr(a*X+b, c*Y+d) = Corr(X,Y) if a and c have the same sign = -Corr(X,Y) if a and c have opposite ...
2
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1answer
24 views

How can I mathematically show the similarity between these 3 plots?

I have 3 3D plots of field strength measured around an antenna. I want to calculate the mathematical similarity between the points of the field patterns. How can I do this? thanks
0
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0answers
23 views

Correlation coefficient, ACF,

In my book it says $\rho_x(h) = \frac{\gamma_x(h)}{\gamma_x(0)}$, which is the definition of ACF, and $\gamma_x(\cdot)$ is the autocovariance. It then should follow (under conditions of weak ...
0
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1answer
19 views

What values to choose for correlation?

To work out correlation I'm using the online calculator : http://easycalculation.com/statistics/correlation.php ...
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0answers
79 views

What do angle brackets ($\langle\rangle$ ) mean in mathematics/statistics (autocorrelations)?

Okay, so the logarithmic return on a stock is given by: $$r_τ (t) = \ln P(t+τ) - \ln P(t),$$ where τ is the interval of time. I have no problem calculating that. My question comes to the following ...
5
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1answer
129 views

Find $\operatorname{argmax}_x \operatorname{corr}(Ax, Bx)$ for vector $x$, matrices $A$ and $B$

This is similar to, but not the same as, canonical correlation: For $(n \times m)$ matrices $A$ and $B$, and unit vector $(m \times 1)$ $x$, is there a closed-form solution to maximize the correlation ...
0
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1answer
15 views

Correlation Based Filter

i found this paper. Im interesting in part 2.3 Feature Weighting. The correlation function is known from wikipedia and almoast clear ( i can write a function to calculate the value :) ) But now i ...
0
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0answers
33 views

Probability Density Function and Eigenvalue Spectrum of Correlation Matrix

My question is in the link... http://www.flickr.com/photos/88684900@N03/8654322505/in/photostream
0
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1answer
43 views

Is the relation of having positive covariance well behaved with respect to taking the inverse?

Let $X$ and $Y$ be two random variables, $X$ strictly positive. Assume that Cov$(X,Y)>0$. Does this imply that Cov$(1/X, Y)<0$? I know that being positively correlated is not a transitive ...
0
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1answer
142 views

special matrix in terms of its covariance matrix

How can we find a matrix $S\in \mathcal{M}_{n,n}$ and $Z\in \mathcal{M}_{n,m}$ whose $n$ entries of the $i^{th}$ column $Z_i$ are correlated $Z_i \sim \mathcal{N}(0,S)$ where $S \in \mathcal{M}_{n,n}$ ...
3
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2answers
57 views

Covariance$(X,Y) \geq 0$ if $X,Y \geq 0$?

I was wondering if you can say something about the covariance of two positive variables $X$ and $Y$?
0
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0answers
58 views

Sum of correlated conditional variables

I have a normal random variable X with mean $\mu_x$ and variance $\sigma_x^2$. I take readings from only X every day (these observations are independent). I have another normal random variable Y ...
0
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1answer
23 views

How to correlate the timestamps of 2 systems?

Whenever I've done (simple) correlation in the past, I've always had 2 sets of data that had "connected" axes: ...
0
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0answers
35 views

Is the correlation function convex or not?

Suppose the function for statistical correlation is a non linear constraint in a non linear programming model: $$ \frac{\sum_{t=1}^T (p_t - \bar{p})(R_t - \bar{R})}{\sqrt{\sum_{t=1}^T (p_t - ...
0
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1answer
45 views

What is the correlation function in multivariable/vectoral case?

I know that the correlation function between random variables $X$ and $Y$ is defined as $$ \rho_{X,Y}=\mathrm{corr}(X,Y)={\mathrm{cov}(X,Y) \over \sigma_X \sigma_Y} ={E[(X-\mu_X)(Y-\mu_Y)] \over ...
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3answers
148 views

What is a direct correlation?

I have two contrary definitions of for the direct correlation between two variables $X$ and $Y$ Their correlation coefficient is close to $1$. There is a direct causal relationship between the ...
0
votes
1answer
27 views

Normal distribution $\rho_{X,Y} = 0 \rightarrow X \bot Y$

Assume $X \sim \mathcal N(\mu_1, \sigma_1^2)$ and $Y \sim \mathcal N(\mu_2, \sigma_2^2)$. If $\rho_{X,Y} = 0$ then $X \bot Y$. Can someone give a hint why this is true ?
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0answers
30 views

Sorting Vectors based on their correlation

This problem [question]: Sort vectors according to their distance between them is about sorting vectors based on the distance between them. What about sorting vectors based on the correlation ...
0
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1answer
44 views

The science of pearson product moment correlation coefficient

I need to compare two sound signals for similarity, I took cross-correlation of both the signals and I got a cross-correlation signal, now I intend to use pearson correlation coeff formula to get the ...
0
votes
1answer
105 views

Pearson Correlation Coefficient Interpretation

Let $X=(1,2,3,...,20)$. Suppose that $Y=(y_1,y_2,...,y_{20})$ with $y_i=x_i^2$ and $Z=(z_1,z_2,...,z_{20})$ with $z_i=e^{x_i}$. Pearson correlation coefficient is defined by formula \begin{equation} ...
0
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1answer
54 views

correlation between two different variables

I am studying stochastic processes and found the next problem: Let $A$ and $\Phi $ be two independent random variables such that $E(A) = 0$, $E(A^2) < \infty$, and $\Phi$ is uniformly distributed ...
0
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1answer
60 views

Intraclass correlations can be negative, yet they are a ratio of two variances (which are positive)

Estimates of intraclass correlations can be negative, yet they are a ratio of two variances -- the variance of the means of the classes to the variance of the entire set of values. What is a neat ...
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0answers
24 views

Iterative Computation of Correlation Coefficient

Given a set of $k$ data points $A$, I have the correlation coefficient between them as $\rho_A$. Now I want to iterate over a new set of data points $B$ (say $j$ of them) and wish to iteratively ...
0
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2answers
34 views

Correlation bound

Let x and y be two random variables such that: Corr(x,y) = b, where Corr(x,y) represents correlation between x and y, b is a scalar number in range of [-1, 1]. Let y' be an estimation of y. An ...
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0answers
30 views

how to compare correlation between random variables?

Suppose I have a random variable, S(k) for starting date of callable bonds, M(k) for the maturity date of the bonds, and C(k) for the called date of the bonds. $$S(k) < C(k) < M(k)$$ C(k) is ...
3
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1answer
160 views

quadratic relationship

Detection of linear relationship is possible with correlation coefficient. If absolute value of correlation coefficient is 1, then the relationship is linear. Is there any way for detecting quadratic ...
0
votes
1answer
44 views

Relationship between Correlation and Bayes Theorem

Is there some relationship between the correlation of two random variables, and Bayes Theorem? A bit of background intuition, if W = random variable denoting number of women in a room, and L = ...
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0answers
19 views

Estimating the likelihood of independence of two discrete variables using the co-occurrence count matrix.

I have some data about users from different regions visiting different directories of some website. Aggregating that data I get the co-occurrence frequency matrix (for regions and directories). Now I ...
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0answers
58 views

Pearson correlation and metric properties

Assuming that the data set was $z$-standardized to zero mean and unit variance (also assuming that it does not contain constant vectors). Then Pearson's r reduces to Covariance: $$\rho(X,Y) := ...
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0answers
34 views

Correlation Coefficient dealing with discretely distributed variables

I'm a bit stuck on this practice problem I have for my HS business stats class. I'd appreciate any help to get the solutions. Thank you. Exercise #22: Let X and Y be discretely distributed random ...
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3answers
604 views

Correlation between three variables question

I was asked this question regarding correlation recently, and although it seems intuitive, I still haven't worked out the answer satisfactorily. I hope you can help me out with this seemingly simple ...
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0answers
83 views

Cross-Correlation (and finding Correlation error ) of two digital sequences.

In a IEEE paper, I saw a formula for WUInt(ti+1) as , Reference : ...
2
votes
1answer
31 views

Find data to perform regression analysis

I'm trying to find some data (two continuous variables that I believe are correlated) online for which I can perform a regression anaylsis, my assignment sheet says: The data may be found anywhere ...
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0answers
61 views

Compute significance of Kendall tau-b?

I have so-far tried all ways of computing kendall tau significance (where there are ties) described here. However, none of them works good, even for relatively large vectors. I think the problem is ...

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