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

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Determinant of a N symmetric square matrix with diagonal 1

What is the determinant of a symmetric $n \times n$ matrix with all diagonals be 1 and all others are $\rho$ (yes correlation matrix)? Anyone can tell me a method to work it out elegantly? Thanks!
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0answers
6 views

Methods for Uncorrelating data - Comparison

I see that both PCA and Cholesky Decomposition could be used for uncorrelating correlated data. When should one be used? What are the assumptions made by each model. When do the methods fail? Are ...
1
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2answers
257 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 ...
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2answers
40 views

Correlation of random variables with joint PDF proportional to $x^{a-1}y^{b-1}(1-x-y)^{c-1} $

The random variables $X$ and $Y$ have joint PDF $$f(x,y)= \frac{\Gamma(a+b+c)}{\Gamma(a)\Gamma(b)\Gamma(c)}x^{a-1}y^{b-1}(1-x-y)^{c-1} $$ where $0 \leq x \leq 1 , 0 \leq y \leq 1, x+y < 1 $ where ...
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2answers
26 views

What is the intuitive meaning of uncorrelated?

I was going through the derivation of the Kalman filter and it mentions that since noise (v) is uncorrelated to the state (x) and the state estimate (xbar), the following quantity is zero: E((x - ...
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0answers
16 views

Checking hand manipulations of matrices

Beginning with a 4*3 matrix: 5 4 -1 2 3 -3 3 4 -4 1 3 -2 I have to perform four manipulations on it, which I did by hand. I wanted to ask if my thinking and/or ...
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0answers
30 views

Integration of shifted symmetric monotone functions

Assume that $f(x),g(x),h(x): \mathbb{R} \rightarrow \mathbb{R}$ are functions with the following properties: smooth symmetric positive monotone decreasing for $x > 0$ Define $g(u,v) = ...
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0answers
18 views

autocorrelation of Ornstein Uhlenbeck process

How to prove that the autocorrelation function of a Ornstein Uhlenbeck process decays exponentially? I.e. for the OU process variance $\sigma^2(t)$ : $\sigma^2(t)=exp(-\lambda ...
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2answers
24 views

Probability of observing a false correlation and confidence limits

In oil and gas exploration/development it is common to use acustic impedance derived from reflection seismic surveys to predict the porosity measured in wells drilled in the reservoir. I often use ...
5
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2answers
2k views

Correlation Coefficient and Determination Coefficient

I'm really new to linear regression and am trying to teach myself. In my textbook there's a problem that asks why R^2 in the regression of Y on X = the sample correlation between X and Y the whole ...
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0answers
14 views

Exponentially weighted rank ordered correlation matrix

Is there any well-known method to apply exponential weighting (similar to EWMA) to rank ordered correlation matrices such as Kendall tau or Spearman?
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0answers
15 views

Generate Correlated Normal and Log-Normal Random Variable

The standard approach for generating two normally distributed random variables some with correlation $\rho$ is explained here: Generate Correlated Normal Random Variables. Now let $X,Y$ be normally ...
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1answer
19 views

Re-calculating Value of $100 in Each State by Specific State

I'm using this Tax Foundations graphic for data. How would I re-calculate each state based on a specific state? For example, what if I wanted to base the control state on Missouri, which is $113.51. ...
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0answers
12 views

Can Pearson's correlation coefficient be computed for 3d surfaces

I have two functions $f(x,y)=z$ and $g(x,y)=z$ given on discrete intervals $x_1,\ldots,x_n$ and $y_1,\ldots,y_n$... In other words, I have 2 matrices of dimension $3\times n$ representing discrete ...
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0answers
11 views

similarities between two binary matrices

I want to measure the similarities between two matrices A and B. Both A and B contains the feature vectors of sounds and are in binary format. i want to see what is the similarities between these two ...
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1answer
527 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 ...
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0answers
27 views

The meaning of correlation coefficient and p-value

I found the following quote in a study, but I'm not sure exactly what it means: Using linear regression, the immunization schedules of these 34 nations were examined and a correlation ...
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1answer
49 views

Determine Patterns

I have some weather data that I would like to analyze. I have about a millions rows of data, and each row has about 100 attribute values. Each attribute value represents some measurement (i.e., ...
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0answers
7 views

Calculate an ensemble average on computer

In a book I am reading, they have the expression $<j_1(u(0)) \, j_1(u(t))>$ where $j_1$ is a first order spherical bessel function. Now I have an expression for $u(t)$ and would like to ...
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2answers
70 views

Autocorrelation function and power spectral density

I want to get the autocorrelation function of the power spectral density of the wind. This function is defined by: $$s(\omega)=\frac{c_1}{(1+1.5 \times c_2\omega)^{5/3}}$$ $c_1$ and $c_2$ are ...
5
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1answer
114 views

Weighing correlation by sample size

I'm a scholar in the humanities trying to not be a complete idiot about statistics. I have a problem relevant to some philological articles I'm writing. To avoid introducing the obscure technicalities ...
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0answers
6 views

covariance and correlation of two three dimentional gaussian distributions

Lets say we have 'n' three dimensional dimensional gaussian distributions with a '3' dimensional mean vector and 3 x 3 non-diagonal covariance matrix. How can I check if they are correlated? Is ...
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1answer
31 views

Sample Size for Correlation Testing

A research team wishes to test the null hypothesis: $H_0, r=0$ at $\alpha = 0.025$ against the alternative: $H_1, r>0$ using Fisher’s transformation of the Pearson product moment correlation ...
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1answer
33 views

Regression with Mean, Standard Deviation, Range and Correlation

A research team collected data on students in a statistics course. Their dependent variable was the student’s score on the final examination, which ranged from 200 to 800 points. The observed average ...
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1answer
19 views

Work out if the relationship between 2 datasets is constant

I have 2 one-dimensional datasets, let's call them a and b. I want to know the correlation between ...
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1answer
28 views

What test should I use to statistically compare two intraclass correlation coefficients (ICC)?

I need to compare two generalizability (G) coefficients for data that are from two separate populations. G coefficients are a type of intraclass correlation coefficient (ICC). The literature on ...
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1answer
36 views

Correlated Rayleigh random variable generation

How to generate 4 correlated random variables Rayleigh distributed with parameter "a" and the co-variance matrix is toeplitz (1 rho rho^2 rho^3) where rho is the correlation coefficient
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2answers
989 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 ...
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0answers
19 views

Help in finding if the relation exist

I have this relation: $$ exp(-\phi \rho ) = \frac{h-1}{n-1} \psi(\phi, \rho ) $$ where $\phi \in [a,b] \subseteq \mathbb{R}^+ \backslash \{0\} $, $\rho \in [c,d] \subseteq \mathbb{R}^+ ...
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1answer
53 views

Summing dependent random variables with unknown joint cdf

Suppose that X_1, X_2,... X_5000 are discrete and dependent non-identically distributed random variables, whose marginal distributions are known, but whose joint distribution is not known. Is there ...
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0answers
9 views

Difference in magnitude between two cross-correlations by two different way of calculations.

I think there are two ways of calculating cross-correlations for two difference random variables, X and Y. I am assuming discrete functions. 1) Multiplication $$ \sum_{m=-\infty}^\infty x[m]y[m+n] ...
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0answers
15 views

Correlation Statistic with a neutral score

I'm trying to develop a correlation statistic to compare lines/random variables (represented as a series of points). I want the correlation value to convey little information if one the lines is a ...
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1answer
30 views

correlation estimator variance

Consider I have realisations of two random variables $X$ and $Y$ and I estimate their correlation thanks to the classic formula : ...
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0answers
23 views

Difference between Kendall tau distance and Kendall tau rank correlation coefficient

What is the difference between Kendall tau distance and Kendall tau rank correlation coefficient? Which one I should use to calculate how similar two arbitrary permutations of ranks are? Suppose, we ...
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0answers
24 views

Correlating random numbers seems to skew the data

I am trying to generate a series of correlated random numbers that represent currency exchange rates for a Monte-Carlo simulation. I am attempting to do this via a Cholesky decomposition of the ...
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1answer
28 views

How to calculate the HHG (Heller Heller Gorfine) correlation

HHG (A consistent multivariate test of association based on ranks of distances) is introduced in: Heller, R., Heller, Y., & Gorfine, M. (2012b). A consistent multivariate test of association ...
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1answer
13 views

correlation matching audio files peak position

if i cross correlate an audio file with itself (which means there is no delay or difference), the peak position should be a zero or at the center of the cross correlation? that is really confusing ...
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1answer
25 views

Convolution module

I am trying to apply GCC-PHAT algorithm here to process audio files and find delay between them. Im coding using Android and Java with the help of this library, and comparing the results with Matlab. ...
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1answer
22 views

Comparing ranking algorithms

If I have several different ranking algorithms and a 'correct' ranking, is there a good way of "scoring" the alternative rankings given by the algorithms against the reference one? For example: ...
2
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0answers
41 views

Expectation and convolution question.

I am learning in an image processing course, and the professor did the following: As part of a derivation, has this: What I do not understand, is how he was able to remove $r(i,j)$ to the ...
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1answer
27 views

Correlation coefficient of i.i.d variables

Let $X_1, X_2, X_3, ...$ be i.i.d variables, and for every $i$ $X_i$ has variance. Define $S_k=\sum_{i=1}^{k}X_i$. Calculate $\rho(S_m,S_n)$ for $m\leq n$. Well, I know it should be $\sqrt{ m/n }$, ...
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2answers
36 views

Correlation coefficient calculation

Why do we remove of the mean of the data while calculating the correlation coefficient value of bivariate data in statistics? DotProduct/ProductOfLengthOfVectors should always give anyway a ...
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2answers
33 views

Finding the correlation coefficient of ordered statistics

I am working on the following problem. Let $$X_{(1)}, \ldots ,X_{(n)}$$ be the order statistics from the uniform distribution of $[0,1]$. Find the coefficient correlation of $X_{(1)}$ and ...
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0answers
14 views

factor analysis for given data

suppose that we have following data i have done covariance matrix and eigenvalue decomposition ...
1
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1answer
40 views

How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$?

Suppose we have a time series $X_t$ s.t. $X_t \sim^{iid} (0,1)$. How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$? Or, I guess, if ...
1
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1answer
95 views

Does $0$ correlation imply independence for marginally normal distributions?

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
27 views

Multiple correlation

My question is very elementary. I need to implement a software that computes the multiple correlation of a set of datas that I have. In order to do that, I need would like to find the generic formula ...
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1answer
33 views

How can you compare two mathematical functions of single variable? [closed]

I have some functions and want to see how close one function is to the other. One way to check is correlation. What are the other ways of checking the "similarness", "closeness" or "nearness"?
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1answer
342 views

Correlation Coefficients with Unequal Data Sets

I would like to determine the correlation coefficients of two timesets of data with unequal entries to detemine how often they move together. I am performing the following computation but would like ...
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1answer
24 views

Mutual information decrease with coarse-graining

Let $X,A,Y,B,C,D$ be random binary variables. $D$ is independent from $X,A,C$ and $C$ is independent from $Y,B,D$. Is it true that: If $I(Y:B|D=0)\leq \epsilon$ then $I(X\oplus Y:A\oplus ...