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Results tagged with copula
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user 27403
A copula is a multivariate distribution with uniform marginal distributions. Copulas are mostly used to represent or to model the structure of dependence between random variables, separately from the marginal distributions.
28
votes
Accepted
Attainable correlations for lognormal random variables
Comonotonicity and countermonotonicity
The random variables $X_1, \ldots, X_d$ are said to be comonotonic if their copula is the Fréchet upper bound $M(u_1, \ldots, u_d) = \min(u_1, \ldots, u_d)$, which … The random variables $X_1, X_2$ are said to be countermonotonic if their copula is the Fréchet lower bound $W(u_1, u_2) = \max(0, u_1 + u_2 - 1)$, which is the strongest type of "negative" dependence in …
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5
votes
Accepted
Understanding tail dependence coefficients
For example, the Gumbel copula with parameter $\theta = \log(2)/\log(1.5)$ has
a coefficient of upper tail dependence equal to $0.5$. … The data were generated with the copula package in R (code is provided below).
## Parameters
theta <- log(2)/log(1.5)
n <- 1000
## Generate a sample
library(copula)
set.seed(234)
gumbel.cop <- …
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27
votes
How to simulate from a Gaussian copula?
There is a very simple method to simulate from the Gaussian copula which is based on the definitions of the multivariate normal distribution and the Gauss copula. … Gauss copula
The Gauss copula is defined implicitely from the multivariate normal distribution, that is, the Gauss copula is the copula associated with a multivariate normal distribution. …
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1
vote
Joint distribution of two sums of correlated variables
The distribution of the sum of independent random variables/vectors can often be obtained easily using moment generating functions (MGF).
In short, the MGF of the sum is the product of the MGFs of th …
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