For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].
2
votes
1answer
110 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 ...
1
vote
1answer
206 views
Linear vs non-linear Correlation
How do i check that two random variables satisfy the requirements for computing correlation via Pearson or Spearman? If the data is non-linear/ non-Monotonic, are there other tests i could use to ...
1
vote
1answer
45 views
Long time scale correlation
I have some EXTREMELY noisy data (standard deviation a is greater than the mean), but plotting it with a 15 data point running average does well to get a visual indication of the trending. I want to ...
1
vote
1answer
326 views
Correlation between Beta distributions
I have a Computer Science background and not very knowledgeable in Probability and Statistics. So excuse me if my question,notation, or language is flawed. Anyways, the problems is that we have two ...
0
votes
1answer
90 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
votes
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
...
0
votes
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
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 ?
0
votes
1answer
40 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 = ...
4
votes
0answers
39 views
PCA vs Correlation
What is the relationship between (first) principal component(s) and the correlation matrix or the average correlation of the data. For example, in an empirical application I observe that the average ...
3
votes
0answers
100 views
How to perform nonlinear regression with correlated errors?
I have a nonlinear least squares problem, but the errors are correlated. I could use R's nls function to do the regression if the errors were independent, but I don't know the right way to handle ...
2
votes
0answers
16 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.
...
2
votes
0answers
49 views
Correlation between an event and a time series
I have a time series, e.g. the daily number of visitors on my blog. I have a set of events of some class, like the days when I made a new posting. I want to measure the effect of a new posting on the ...
2
votes
0answers
103 views
Correlated diffusion processes and covariance matrix
I'm really noob in maths topics so I hope you will excuse me if I use terms which aren't correct.
I would like to simulate $n$ dimensional diffusion processes with $n$ noises.
Each process has its ...
2
votes
0answers
167 views
Geometric interpretation of element by element division of one vector by another
This is my first post here, and I'm not a mathematician, so please go easy on me :)
In statistics there is a geometric interpretation of correlation that uses basic vector geometry. This is fairly ...
2
votes
0answers
524 views
Correlation and Regression Question
Two separate tests are designed to measure a students ability to solve problems. Several students are randomly selected to take both tests and the results are:
$$
\begin{matrix}
\text{Test A}(x) ...
1
vote
0answers
13 views
Dimension free Concentration bounds for Martingales
Consider the following random process which is defined on $n$ numbers $0\leq x_1,\ldots,x_n\leq 1$:
At each step, pick an arbitrary number, say $x_i$. Then randomly (and independently) change its ...
1
vote
0answers
28 views
Sorting Vectors based on their correlation
This problem [question]: Sort vectors according to their distance between them is about sorting vectors based on the distance between them. What about sorting vectors based on the correlation ...
1
vote
0answers
18 views
Estimating the likelihood of independence of two discrete variables using the co-occurrence count matrix.
I have some data about users from different regions visiting different directories of some website. Aggregating that data I get the co-occurrence frequency matrix (for regions and directories). Now I ...
1
vote
0answers
43 views
Pearson correlation and metric properties
Assuming that the data set was $z$-standardized to zero mean and unit variance (also assuming that it does not contain constant vectors).
Then Pearson's r reduces to Covariance:
$$\rho(X,Y) := ...
1
vote
0answers
75 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 :
...
1
vote
0answers
59 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 ...
1
vote
0answers
89 views
Windowed Linear Correlation
$\DeclareMathOperator \Cov {Cov}$
$\DeclareMathOperator \Var {Var}$
$\DeclareMathOperator \E {E}$
Consider the following experiment:
For $N\geq1$, consider $N$ black balls. Let us paint each black ...
1
vote
0answers
21 views
Dynamic Light Scattering
In DLS does the combination of the Time Average and Ensemble Average give a better statistical average than the results shown by each case considered separately ?
1
vote
0answers
113 views
Cross Correlation
The cross-correlation function is defined as follows if $\bar{f}$ is the complex conjugate of $f$ and we assume that $f$ is real, such that $\bar{f} = f$.
$$
\begin{align}
f \star g &= ...
1
vote
0answers
36 views
Sampling a distribution with restrictions: eliminating the correlation between two variables
I have a collection of 400.000+ word-pairs. Each word-pair has an association strength, which is a measure of how related the two words are to each other (as in cow-milk). Each word-pair also has a ...
1
vote
0answers
91 views
Correlated Random Numbers Between A Range
I am trying to generate random numbers within a range say 57 to 107 which are correlated by a factor of 0.8. The numbers are for illustration simplicity only.
0
votes
0answers
16 views
Calculate the tendency of a set of samples
I develop an application in which I constantly get samples of heart pulse.
I defined an interval of $t$ seconds.
In each $t$ seconds I have $n$ samples.
In every interval, I want to calculate the ...
0
votes
0answers
16 views
Correlation question
I hope someone can help me with this:
Let $c(\rho)=\lim_{n\rightarrow\infty}n^{\alpha-1}\sum_{k=-(n-1)}^{n-1}\left[1-\frac{k}{n}\rho(k)\right]$ where $n=1,2,3,\ldots$, $\alpha\in(0,1)$ and $\rho$ is ...
0
votes
0answers
39 views
Invariance of the correlation coefficient under linear transformations
Show that for arbitrary random variables X and Y, and constants a ,b ,c ,d with a and c nonzero, Corr(a*X+b, c*Y+d) = Corr(X,Y) if a and c have the same sign
= -Corr(X,Y) if a and c have opposite ...
0
votes
0answers
19 views
Correlation coefficient, ACF,
In my book it says
$\rho_x(h) = \frac{\gamma_x(h)}{\gamma_x(0)}$, which is the definition of ACF, and $\gamma_x(\cdot)$ is the autocovariance.
It then should follow (under conditions of weak ...
0
votes
0answers
54 views
What do angle brackets ($\langle\rangle$ ) mean in mathematics/statistics (autocorrelations)?
Okay, so the logarithmic return on a stock is given by:
$$r_τ (t) = \ln P(t+τ) - \ln P(t),$$ where τ is the interval of time.
I have no problem calculating that. My question comes to the following ...
0
votes
0answers
25 views
Probability Density Function and Eigenvalue Spectrum of Correlation Matrix
My question is in the link...
http://www.flickr.com/photos/88684900@N03/8654322505/in/photostream
0
votes
0answers
53 views
Sum of correlated conditional variables
I have a normal random variable X with mean $\mu_x$ and variance $\sigma_x^2$. I take readings from only X every day (these observations are independent). I have another normal random variable Y ...
0
votes
0answers
33 views
Is the correlation function convex or not?
Suppose the function for statistical correlation is a non linear constraint in a non linear programming model:
$$
\frac{\sum_{t=1}^T (p_t - \bar{p})(R_t - \bar{R})}{\sqrt{\sum_{t=1}^T (p_t - ...
0
votes
0answers
20 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
votes
0answers
28 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 ...
0
votes
0answers
33 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 ...
0
votes
0answers
96 views
Autocorrelation derivation using fourier transform
I am stuck with basic understanding of the Auto-correlation derivation of a simple signal and I would be pleased if you could help me out with that.
Lets have a signal $x(t)=\cos(2\pi{f_{0}}{t})$.
...
0
votes
0answers
51 views
How to find function coefficients
I'm not an expert in math but I need to solve the following task:
I have several functions:
$$
f(t)=k_1 f_1(t)+k_2 f_2(t)+k_3 f_3(t)+ \dotsc +k_n f_n(t)
$$
Also I know all the functions' values: ...
0
votes
0answers
50 views
Min and Max Correlation values
i want to know whats is the max value that the correlation rho can take :
$\mbox{Rho}(u_1,u_2) = \mbox{Cov}(u_1,u_2)/(\sigma_1*\sigma_2)$
where $u_1$ is a uniform random Variable and $u_2$ is an ...
0
votes
0answers
57 views
Is shift-invariant property of (auto) correlation function so important?
I was just wondering if the shift-invariant property of autocorrelation function is important. No matter random process is wide sense stationary or not, can we overlook the shift-invariance of ...
0
votes
0answers
204 views
jointly stationary random process
If two wide-sense stationary processes $X(t)$ and $Y(t)$ are uncorrelated, then the cross correlation is
$R_{XY}(t_1,t_2) = E\{X(t_1)Y(t_2)\} = E\{X(t_1)\}E\{Y(t_2)\}$,
which will be a constant, ...
0
votes
0answers
47 views
Determining how much closer a sequence is to another series?
I am supposed to make a game in which a range of numbers starting from 1 are scattered across the screen and the player has to click them in series. Somewhat like this but much less range,
You have ...
0
votes
0answers
144 views
Combine dependent variables into index that best matches independent variable?
I'm an undergrad working in a geochemistry lab for the summer. My job requires a good amount of statistical analysis, something that I'm not very familiar with.
I'm looking for an way to blindly ...
0
votes
0answers
51 views
Controlling auto-correlated 1D Brownian motion
I have 1D Brownian motion process $x(t)$, and ability to control it.
The control allows to shift the $x$ by $D$ at any time.
I need the controlled process to be zero-mean, and to use the control ...
0
votes
0answers
27 views
Fast approximate construction of orthogonal system
Assuming I have $d+1\in\mathbb{R}^d$ points that are not unfortunately chosen (in which case I can just resample, correct me if I $d$ points are enough), then these should span the whole space.
What ...
0
votes
0answers
172 views
How to find a correlation and whether it is statistically significant
I have 2 columns with numers in them, x and y. I'd like to find out what y could be if x = n and how strong the correlation is, if it's statistically significant or not.
How do I do that?
Pretty ...
0
votes
0answers
554 views
Pseudo-random binary sequence generated by shift register
Binary sequence generated by shift register with feedback have periodic properties. A simple 4-bit shift register shown in Fig (a). For the initial condition shown, it can be verified that the ...
0
votes
0answers
39 views
Finding out whether or not two graphs are “close”, given 20 points on each graph whose Xs do not match
Let's assume we have two graphs where:
Each graph has 600 points per minute.
We're allowed to get only one point per minute.
We do not get the same point per minute in both graphs. So for example, ...
