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

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86 views

Correlated variables from Latin Hypercube

Say I have a vector $\mathbf{Y}$ of $n$ normally distributed random variables. I have its mean vector $\mu$ and covariance matrix $\Sigma$. Normally if I were to generate a sample, I would decompose ...
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37 views

Generate two sets of (nonlinearly) dependent random numbers

I would like to find a method to generate two sets of (nonlinearly) dependent random numbers. Solution for linear dependence (that is, correlation). Generate two sets of uncorrelated random numbers ...
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1answer
55 views

Combination problem: random selection in a group

A scientific committee of 4 persons is to be randomly selected from a group consisting of 3 biologists, 3 physicists and 4 mathematicians. Let X denote the number of biologists, Y the number of ...
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34 views

Best line fit for correlated points

Given in $\mathbb{R}^3$ are $n$ points $\mathbf{y}_i\sim N(\mathbf{y}_i-\mathbf{\hat{y}}_i, \mathbf{C}_i)$, which are normally distributed. I want to determine a best fit line $\mathbf{u}(\lambda) = ...
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0answers
14 views

Is auto-correlation a particular and simple form of pattern in time series?

In a time serie context and considering the sign of the variation of the variable auto-correlation means that for couple of measures at (time t, time t+1) the ...
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0answers
36 views

OLS standard error that corrects for autocorrelation but not heteroskedasticity

Question: By mapping the OLS regression into the GMM framework, write the formula for the standard error of the OLS regression coefficients that corrects for autocorrelation but not ...
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28 views

correlation between numeric, boolean, percentage

Let's say that I have several series of results. And I'd like to calculate correlation between them. The problem is that they are represented in different units (numeric, boolean,percentage). For ...
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1answer
26 views

Is $d(i,j) = 1-\textrm{corr}(i,j)$ a metric?

I need to make sure that this function is a metric: $d(i,j) = 1-\textrm{corr}(i,j)$ where $\textrm{corr}(x,y)$ is the Pearson correlation coefficient which ranges from $[-1,1]$. With this scaling I ...
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27 views

Bounding the Correlation Coefficient

Let us assume we have two random variables $X$ and $Y$ where $X = f(A, B, C)$ and $Y = g(A, B, C)$. $A, B, C$ are 3 independent random variables and the functions $f, g$ are known but rather expensive ...
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56 views

Difference between identity and diagonal covariance matrices

thanks in advance for the help. Suppose I am training a linear model. What are the conceptual differences between using a diagonal covariance matrix and the identity? It is clear to me that the ...
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1answer
19 views

Covariance matrix computed based on a covariance function

I am reading Chapter 4 of Gaussian Processes for Machine Learning. It says that a matrix $K$ whose entries are computed as $k_{ij} = k(x_i, x_j)$ where $k$ is a covariance function is a positive ...
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1answer
62 views

Constraints on correlation coefficients of multiple random variables

I am looking for a generalization of Correlation between three variables question for more than three variables. It is stated in one of the answers there that, for three variables with pairwise ...
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24 views

Test indipendence and stationarity

I have to apply a model on a dataset of $I$ variables, each one with $n$ observations, but I need that every variable is stationary and indipendent from the other ones for the model to work. My ...
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2answers
45 views

How to find relation between 2 numbers

I have been practicing programming for many months now and what I found difficult is not about solving problem. But it is how to find the "how to solve problem" to make computer solves that for me! ...
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0answers
37 views

Error propagation in pearson correlation

I have two data-sets $X$ and $Y$ with errors $\Delta X$ and $\Delta Y$. I calculated the Pearson Sample Correlation $r$. Is it possible to calculate the error of $r$ using propagation of uncertainty: ...
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0answers
12 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 ...
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2answers
46 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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0answers
35 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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2answers
59 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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23 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
47 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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2answers
38 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 ...
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1answer
20 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
79 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
31 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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0answers
22 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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1answer
55 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
13 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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2answers
148 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 ...
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1answer
69 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
140 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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1answer
51 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
25 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
92 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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1answer
64 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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0answers
35 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 ...
0
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1answer
90 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
85 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
30 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
38 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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1answer
35 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
38 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. ...
2
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0answers
107 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 ...
0
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1answer
101 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
44 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 ...
1
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1answer
47 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 ...
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2answers
65 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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0answers
31 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
38 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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2answers
38 views

What is this idea of “Minimum Correlation”?

So I was having a read of this paper here: Minimum correlation for any bivariate Geometric distribution. On the first page of he paper we encounter the following definition of "minimum correlation": ...