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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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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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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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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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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37 views

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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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 ...
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Bivariate random variable with R [closed]

I am trying to transform this Matlab code into R. My goal is to generate a bivariate random variable with a pre-specified correlation. The code uses the idea of t-copula. I can't figure out how to ...
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Generating values from copula using copula package in R

I have a bunch of questions concerning the use of the copula package in R. My overall aim is to generate synthetic values using copulas. I am analyzing a hydrological data: annual peak discharge ...
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How to find conditional probability P(X<x|Y=y) using copulas?

I am trying to find conditional probability of the form P(X<x|Y=y) for two jointly distributed random variables based on the copula estimate from training data. ...
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How to find a conditional probability using copula-based Markov process?

I have a monthly time series of a water quality parameter. I used copula-based Markov process of C(Y(t), Y(t-1) and I forecasted the mean behavior of Yt by following equation: Now, I need to find ...
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What are $\rho$-, $\beta$-, and $\alpha$-mixing conditions?

I have seen properties named $\rho$-, $\beta$-, and $\alpha$-mixing conditions in papers related to Copulas and Markov processes like this one: In this paper, we identify conditions on $C$ that ...
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Fitting a copula with Poisson marginals to data in R

First off, I know this is a question which requires an thorough answer, so I am coming here with a very humble attitude. I have limited knowledge about both copulas and R, so I will try to explain ...
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Help understanding uniform marginal distribution in Farlie-Morgenstern family.

http://imgur.com/FeFf3e9 The imgur link is to a screenshot of the relevant section in my text. I have trouble understanding how if $H(x, \infty)=F(x)$ is the marginal distribution of $x$, how $F(x) = ...
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What is copula transformation

I have seen that copula transformation changes my sample space to the range of $[0 \; 1]^d$ where d is the number of dimensions. Can anyone explain me about copula transformation?
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Struggling with copula theory

I'm really struggling with bivariate copula's. Long story short, I can only use Gaussian copulas. I'm therefore interested in the joint PDF for which the Gaussian copula can be applied. So for ...
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Generating samples from Copula in R

Suppose I want to model dependence between $d$ r.v.´s $Y_1,...,Y_d$ with the copula $C_\theta$, where $\theta$ are the corresponding parameters of that copula. I've also determined the correlation ...
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Generating Random Vectors with Arbitrary Marginal Distributions via NORTA

When generating random variates from different marginal distributions using the NORTA (Normal-to-Anything) method, as described in Cario & Nelson 2007, why is $\varrho$ required? To adjust ...
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How to generate from the copula by inverse conditional cdf function of the copula?

I am trying to write a code (I am using MATLAB) for estimating the goodness of fit of the copula based on a Rosenblatt transformation ( Dobrić and Schmid 2007, ...
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Plot of copula (based on data set) - R

I have to do an empirical analysis for a statistics paper. For this I want to show the differences of dependence structure for a specific data set. So I selected 2 stock prices, transformed them into ...
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Understanding tail dependence coefficients

How can I analyze the $\lambda_U$ and $\lambda_L$ results (estimated by non-parametric method)? What does higher or lower coefficients mean? Does $\lambda_U = 0.5$ mean there's some kind of linear ...
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Generate correlated multivariate normal samples with copula

I've seen examples of constructing multivariate distribution with univariate marginals coupled together via a normal copula (see Mvdc function from copula package ...
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Fitting copulas with a given covariance matrix

Suppose that I have a new way of estimating covariance matrice (from a particular data set), and that I believe this is better than the sample covariance matrix. I want to fit a t-copula with this new ...
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What is an adaptive copula?

My basic question is: What is an adaptive copula? I have slides from a presentation (unfortunately, I cannot ask the author of the slides) about adaptive copulae and I am not getting, what this means ...
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Why is this representing the left tail?

In this source about the Clayton copula on page 18 they write: It has been used to study correlated risks because it exhibits strong left tail dependence and relatively weak right tail ...