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.

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Inverse of a conditional CDF involving Copula

I am planning a Monte-Carlo simulation exercise involving Gaussian Copulae. I have $n$ random variables $X_1,X_2,X_3,...,X_n$ with known CDFs $F_i(x)$ (the CDFs are known but can not be described by ...
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Copula compatibility problem

Suppose I have a 3-Copula which I would like to construct with two 2-Copula's, as the following construct: $$ C_2(u, C_1(v,w)) = C(u,v,w) $$ My question is, if $C$ is known to be a valid copula ...
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How to compute joint cdf of an empirical copula? (Updated with more info)

lets suppose a bivariate empirical copula as: for a set of data of example data we can plot it like this: How can we compute the joint cdf of this empirical copula which should like this: Thank ...
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Question with Copulas

I've come across this question in my class which I'm struggling with. If we have the copula $C(u_1,u_2)=\phi^{-1}(\phi(u_1)+\phi(u_2))$ where $\phi(u) = (-\ln (u))^{\gamma}$ for ${\gamma} \ge 1$, ...
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What is the joint CDF of a Vine copula?

Consider a 4 dimensional D-Vine Copula with the following density function: what will be the joint cdf function? The pdf function is from Aas et al., 2006 ...
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How to do Hierarchical (Nested) Elliptical Copula simulation sampling

dear researchers, I am doing a project to aggregate about 30 risks into total loss (15 of them are market risks, and 15 of them are insurance risks). The current approach is to simulate millions of ...
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Generate FGM copula

In the interest of learning about Copula's, I want to write some Matlab code which generates copula random variables (I realize there exists a toolbox for this, but I don't want to use that). As ...
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How to obtain real observation from simulated pseudo observation? (from the copula)

I have fitted a normal copula to my data in R using the copula package and generated pseudo observation in the unit square [0,1]^2. I am having troubles retrieving the simulated values: how can I get ...
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How do I convert simulated values from a copula to “real” observations? R

I have managed to fit a different kind of copulas to my data in R (mostly Archimedean copulas) using the copula package. I have no problem in simulating pseudo observations (u and v), my questions ...
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What are marginals?

Marginals are mentioned a lot in copula literature, what does the term really mean? For example what is the intuitive meaning behind a statement like "This function describes the dependence ...
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Copulas for generating uniform random variables with correlations

I want to generate uniform random variables which have a correlation structure defined by a graph i.e. a variable is only correlated with its neighbors in the graph and is uncorrelated with the rest ...
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Copula - Correlation Help

I need some help with copula. I am using the copula with either the multinormal or the student t kernel. I thought before that when I input in my correlation matrix, if I simulate enough random ...
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How can I generate random numbers from any given copula?

Suppose that I have a 2-dim copula function C(x_1,x_2). How can I generate bivariate numbers from this copula? For specific types of copulas, I can use 'rCopula' function of 'copula' package in R. ...
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Modeling of Multivariate Data

Suppose I have a multivariate data set. For the sake of example, lets say that the dimension of my data set is $p=7$ and I have a matrix which contains samples of this multivariate data set. Now ...
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Proof of the relation between Kendall's Tau and Pearson's Rho for the Gaussian Copula

I know in the case of the bivariate normal distribution Kendall's Tau is given by $$ \tau=\frac{2}{\pi}\arcsin({\rho}) $$ where $\rho$ is Pearson's correlation. Can someone given a derivation of this ...
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Generating random samples with bivariate t-copula

I'm trying to generate a bivariate random sample of the t-copula (using rho = 0.8), without using the "copula" package and its function "rCopula" with method "tCopula". I'm using the following R-code: ...
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Kendall's tau for Clayton Copula

When $\theta =-\frac{1}{2}$ the Clayton copula is given by $C(x,y)=(\sqrt{x}+\sqrt{y}-1)^2$. I've been asked to show in this case that Kendall's tau is $-\frac{1}{3}$. Using $$\rho_{\tau}=4 \int_0^1 ...
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Geometric construction of copula - question regarding C-volume

I am learning about copula's, using Nelsen's book, and more specifically about the geometric method of constructing copula's. The problem is replicated in the following link: ...
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Should simulation from a student-t copula distribution yield the input correlation matrix

I am using mathematica to simulate random variates from a student-t copula distribution. Assuming that I input in the correlation matrix R, after generating a certain number of random variates, should ...
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Inverse CDF sampling for a finite mixture

The out-of-context short version Let $y$ be a random variable with CDF $$ F(\cdot) \equiv \cases{\theta & y = 0 \\ \theta + (1-\theta) \times \text{CDF}_{\text{log-normal}}(\cdot; \mu, \sigma) ...
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Sampling an N-dimensional copula via N independent uniforms

In order to draw a sample from an N-dimensional Gaussian copula, we draw N independent standard Gaussian random variables, form a vector, and multiply it by an appropriate matrix (Cholesky and such). ...
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Sampling from conditional copula under R

this is a follow-up thread dealing with sampling from conditional copulas: Original question (with nice answer by whuber): Sampling from conditional copula Trying to sample from a conditional copula ...
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Data transformation using copulas

I've heard about the use of copulas to transform data. For instance, supposedly it's applied to data that is non-normal to make it look more normal. However, I don't quite understand how this is done. ...
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Portfolio VaR with Copula?

Let the portfolio be given by: $$X=X_1+X_2$$ $(X_1,X_2)$ are dependent through a Copula function $C(u_1,u_2)$, such that the joint distribution is given by: $$F(x_1,x_2)=C(F(x_1),F(x_2))$$ What is ...
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Sampling from conditional copula

I am having trouble finding anything on sampling from conditional copulas. I am only interested in the bivariate case. So, if $C(u,v)$ is my copula, I want to sample from it given a specific ...
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Understanding an integral related to copulas

I am trying to understand the following example 5.1 from page 160 of Nelsen's book "Introduction to copulas". $\int\int_{I^2} M(u,v)dM(u,v)=\int_0^1 u du$ where $M(u,v)=min(u,v)$ is ...
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Find the inverse of function

I have a two variable distribution function which I have to find it inverse. The expression is the following: $H(s,t)=t\log(s) +t - t \log(t); \text{ if } s>t$ given: $v = t -t \log (t)$ and $u = ...
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How to fit Gumbel Copula

I am trying to apply Gumbel Copula in R by using "copula" pkg. The parameter "alpha" of gumbel copula is 1.016. The copula structure is: gum.cop=archmCopula(family="gumbel",dim=2,param=alpha) But the ...
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Built a n-variate distribution with given correlations and specific marginal distributions

I want to built a $n-$variate density with the constrains that all the marginals must be the same (i know the marginal distribution) and the correlation between the component $i^{th}$ and $j^{th}$ of ...
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15 views

Bivariate sampling for distribution expressed in Sklar's copula theorem?

In the univariate case, one can easily sample a distribution via random numbers $u\sim[0,1]$ and plugging into $F^{-1}(u)$. I have a bivariate distribution constructed via Sklar's theorem on Copulas: ...
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Copulas with Regression

Copulas are joint distribution of uniform marginal distributions. Traditionally I have seen examples of fitting a Copula to the data and then simulating from the data. I haven't seen much on Copula ...
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Limits on conditional expectation with normal margins and specified (Pearson) correlation

I saw the following question on another forum: "Suppose that both height and weight of adult men can be described with normal models, and that the correlation between these variables is 0.65. If a ...
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Is there any Goodness of fit tests for Vine copulas?

Is there any goodness of fit tests like those based on probability integral transform (PIT) of Rosenblatt available for Vine copulas as a built in function in R? I know we can use ...
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Archimedean copula parameters?

Using R, I am attempting to fit data for 3 stock indices using 3 Archimedean copulas, Frank, Gumbel or Clayton. What are their parameters? In class, we were taught to fit a t copula. Its parameters ...
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Copula estimation

I want to fit a copula distribution. My question is: Is it equivalent to estimate the marginal distributions using marginal samples and later estimate the parameters of a copula to estimating all the ...
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In definition of gaussian copula does the marginals also have to be gaussian?

I am quite new to this copula idea. In particular I am confused about the definition of a Gaussian copula. For a copula to be a Gaussian copula does the marginals have to Gaussian as well? Or it can ...
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What is the difference between elliptical Gaussian and multivariate Gaussian distributions?

I am reading about Metaelliptical copulas but I don't know the difference between elliptical Gaussian and multivariate Gaussian distributions I would appreciate if somebody can explain the difference ...
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Estimating nested copula parameters in R

Using the R copula package, is there a built-in way to estimate the theta parameters of a nested Archimedean copula (ideally together with the marginals) based on empirical data? In the non-nested ...
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Is $H=\min(t_1,…,t_n)$ a Copula?

Please help me prove the following: n-Box is defined as $B=[a_1,b_1]\times[a_2,b_2]\times[a_3,b_3]\times...\times[a_n,b_n]$ Cartesian product of $n$ closed intervals, where $a_i$ and $b_i$ are all ...
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Solutions to exercises in Nelsen's “An Introduction to Copulas”

I am paving my way through Roger Nelsen's "An Introduction to Copulas". The book has exercises (quite good actually), but no solutions. Does anybody have a solution manual for (some of those) ...
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How can I generate ensembles using Copula?

I just got buried in a mountain of math and papers, and I am so confused. So basically, I have data (Probabilistic QPE) from which I have extracted 99 quantiles (1%, 2%, ... 100%) to sample the CDF ...
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Gumbel Copula generation using nonparametric correlations like Kendall's tau

I have 2 different variates W,X. I want to compute Gumbel copula for these variates. I followed following steps for the same: 1. To compute kendall's tau I used R's package Kendall. From kendall's tau ...
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211 views

Copula generation (Gaussian, t and Gumbel) with the help of correlation matrix using R

I have a set of data of 2 variates. I have generated correlation matrix between the variates. Using copula package of R, I computed t-copula using correlation ...
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Model multivariate time series with copula - concepts

I have a question regarding some time series concepts: Suppose I have some "time series" data with cross correlation. Suppose I am able to fit a copula, say to capture dependencies between data of ...
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Using copulas to sample a probability distribution

Say I have two random variables, X and Y. Their joint probability density function is a uniform distribution inside the triangle with vertices at (0,0), (0,1) and (1,2). The area is 1 so the joint pdf ...
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141 views

Tail dependence and copulas

I have been given this formula for upper tail dependence and read that tail dependence depends on the copula and not the marginals: $$ \lambda_U = \lim_{a \to 1} \Pr[Y>F_Y^{-1}(a)\mid ...
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Are Archimedean copulas useless for representing multivariate data?

Following Hofert et al.'s paper "Likelihood inference for Archimedean copulas in high dimensions under known margins," (http://dl.acm.org/citation.cfm?id=2263953) I wrote a script in Matlab to produce ...
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Aggregation of correlated variables

I've been trying to aggregate correlated time series, by using Alexander's proposal that you can see here: http://bit.ly/1hIPwiI. Her proposal to find a random variable $Y=\sum_{i=1}^N X_i$, where ...
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102 views

How to calculate P(X=x|Y=y) using copula functions? [duplicate]

I want to get the conditional probability of P(U=u|V=v) or P(X=x|Y=y) using copulas.However, I found that if I use the copulapdf function of Matlab, the result is bigger than 1! I don't know why. any ...