Linked Questions
10 questions linked to/from Attainable correlations for lognormal random variables
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If LN(X1) is N(0,1) but LN(X2) follows N(0,4), their Pearson correlation is -0.09<p<0.66, not -1<p<1. What's the math behind the result? Sources? [duplicate]
He told me that he saw this in a book by Practical Econometrics by Carol Alexander.
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Generate pairs of random numbers uniformly distributed and correlated
I would like to generate pairs of random numbers with certain correlation. However, the usual approach of using a linear combination of two normal variables is not valid here, because a linear ...
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Generating correlated distributions with a certain mean and standard deviation?
Given a distribution A with a mean of $\mu_1$ and standard deviation of $\sigma_1$, how can I generate:
Distribution B with a mean of $\mu_2$ and standard deviation of $\sigma_2$ and a correlation of ...
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For what kind of distributions could the joint distribution be determined uniquely by marginal distribution and correlation?
Assume $X$ and $Y$ are from the same distribution $P$ and $\rho = \frac{Cov(X,Y)}{\sqrt{Var(X)Var(Y)}}$ is fixed. For what kind of $P$ can we determine uniquely the joint distribution of $X,Y$?
I know ...
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Attainable correlations for exponential random variables
What is the range of attainable correlations for the pair of exponentially distributed random variables $X_1 \sim {\rm Exp}(\lambda_1)$ and $X_2 \sim {\rm Exp}(\lambda_2)$, where $\lambda_1, \lambda_2 ...
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Is a log transformation of predictors a suitable way of dealing with multicollinearity in multiple regression?
Suppose two independent variables in the linear regression initially have very high correlation of 0.95. This introduces severe multicollinearity into the model (as indicated by very high variance ...
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Not all positive-definite matrices are valid covariance matrices for lognormal variables
A simple method to generate correlated lognormal variables $X_i$ that obey a covariance matrix $C_{\mathrm{ln}}$ with elements $c_{\mathrm{ln}}^{ij}$ is to first compute the covariance matrix $C_{\...
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How are bivariate lognormal parameters related to the underlying normal parameters?
If $Y∼N(μ,σ^2)$ is normally distributed, then $X=\exp(Y)$ is lognormally distributed. The parameters for a univariate distribution, $\mu$ and $\sigma$ of this lognormal distribution are given by
$$\mu{...
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Impact of correlation bounds for Monte Carlo simulations
As the lognormal distribution imposes bounds of attainable correlations as discussed in Attainable correlations for lognormal random variables my question would be what happens if say we want to do a ...
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How can we simulate the sensitivity of Pearson correlation coefficient to the distributions of variables? [closed]
I want to make a simulation experiment on the sensitivity of Pearson correlation coefficient to the distribution types of variables. In other words, I want to demonstrate "when the distributions ...
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