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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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Sampling a conditional joint distribution of continuous random variables using samples from joint distribution and marginal distributions

I am seeking an approach to sampling conditional joint distribution (new to probability). I will put my case in a simple way: Similar question for discrete variables is asked Here but not yet ...
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Correct Interpretation of copula contour plots

Going into exploratory data analysis with the intention of fitting copula models, I was looking at the famous copula and they mention here that either contour or 3D ...
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Approximation of copulas

I'm studying copulas, finished the Introduction to Copulas by Nelsen. I'm interested in the latest/best known/etc approaches for approximating any Copula, or some families of copulas, so would be ...
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Default vs recovery rate - gaussian copula

I am trying to link defaut with recovery rates by using a Gaussian copula. My marginals follow a beta distribution. I would like to prove that the usage of a gaussian copula is good choice compared to ...
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Why do we use a criterion like AIC for Copula model selection?

If we look at the AIC formula: AIC = -2*log(ML) + 2k where k is the number of parameters in the model and is considered as the 'penalizing term' for complexity or over-fitting. Does this ...
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Skewed t copula model for multivariate

I recently try to write the code of multivariate skewed t copula model. but I do not have the right function of the model. may I ask for the right function or the matlab code of the model? thanks a ...
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Is there a reason most of author assumed i.i.d in copula models.

I read many of copula articles. I almost found that the authors assumed the i.i.d observations in copula models. I just wonder if there is a reason for this assumption? I searched this site and found ...
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Estimation of copula parameters for $C(u, v) = \min(u^a,v^b)\min(u^{1-a},v^{1-b})$

Given a bivariate copula, say $C(u, v) = \min(u^a,v^b)\min(u^{1-a},v^{1-b})$, $0 < a,b < 1$, how would we use the method of maximum likelihood to estimate the copula parameters, in this case $a$ ...
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Finding probability of a point using bivariate copula density

I have a data in the form $\textbf{N} \times 2$. I am using bivariate copula to model the joint density of this distribution. Firstly, I fit 2 marginal distributions independently on each column of ...
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Why do Gaussian copula does not have a closed form? hence, why numerical estimation is needed?

I am working on Gaussian copula. I always read that, Elliptical copulas do not have closed form expression and hence, the numerical estimation is needed. I really do not understand what does closed ...
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38 views

Calculate the implied correlation for missing cells in a correlation matrix in R

I have a correlation matrix in R. Many of the correlations are specified, but there are some that are "NA". eg, A __ B __ C A 100% NA 25% B NA 100% 50% C 25% 50% ...
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Questions about tail dependence of copula and copula parameters?

I would like to understand tail dependence and its relationship to the copula function. The relationship between copula and tail dependence can be expressed as: (from this question Understanding ...
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Trying to wrap my arms around copulas

This topic is dense with notation that makes things a bit confusing. But is this the correct interpretation? Suppose we have two jointly distributed random variables – $X$ and $Y$ – of arbitrary (...
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Fréchet Hoeffding bounds for symmetric random variables

(Edited to clarify the question). The Hakan & Demirtas (2012 doi: 10.1198/tast.2011.10090) approach to approximating Pearson correlation bounds uses the concept of the Fréchet-Hoeffding bounds by ...
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How do I sample arbitrary probability mass functions? (Archimedean Copula)

I'm trying to use an algorithm (Marshall, Olkin) for exchangable archimedean Copula to generate realizations of multivariate probability distributions. One step includes sampling V which is F ...
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How to derive a set of x and y lead to a given return period in multivariate distribution function

I constructed a multivariate distribution function using the copula package in R. I can successfully derive the cdf of a matrix of observational data. Now I want to find out the data associated with a ...
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Writing syntax for bivariate survival censored data to fit copula models in R

Am required to fit copula models in R for different copula classes particulary the Gaussian, FGM,Pluckett and possibly Frank (if i still have time). The data am using is Diabete data available in R ...
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Does assumption of normality of each mixture components implies that each margins is normal

I just would like to understand some information about the joint normality and the margins. I read that the normal joint distribution almost always implies that the univariate margins are all normal. ...
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Copula and non-Copula models

I am working with copula-based models. Copula models allow to models the margins separately from the dependencies structures. However, non-copula models do not allow for such separation. My question ...
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Does the distribution of each mixture components have any information of the margins of the variables? [closed]

I just start working with Gaussian mixture models and I just confused about some information, which I really would like to make sure that I understand the model very well. A Gaussian mixture model ...
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Simulation of t copula in Python

I am trying to simulate a t-copula using Python, but my code yields strange results (is not well-behaving): I followed the approach suggested by Demarta & McNeil (2004) in "The t Copula and ...
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32 views

Copulas with tail dependence only when correlation non-zero?

I'm wondering if I can get the best of both worlds of the Gaussian and T copulas (and if not, why not?). A property of the Gaussian copula that I like is that if the off-diagonal entry into the ...
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An example of a bivariate distribution with normal marginals and a nonlinear conditional mean curve? [duplicate]

That is, an example of a bivariate distribution with normal marginals for which a linear regression is inappropriate. Does an asymmetric copula always produce this?
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How to use Copulas to Combine Multivariate Conditional Probability with Univariate Conditional Probability?

This is sure to be an odd one, but here goes. I'm trying to estimate P(X|Y, Z) by the distributions of P(X|Y) and P(X|Z). I've thus far been trying to using copulas to achieve that aim, but I'm not ...
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When modeling a copula, you need to generate “pseudo observations”? Why? What is a pseudo observation? [closed]

I'm struggling with the concept of a "pseudo-observation." I can't find any material out there describing what it is in a simple, concise manner. Does it have something to do with observation's ...
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What is the differences between estimating the margins and transforming them using cumulative distribution function

In copula models, the estimation of copula parameters is based on the pseudo-observations of the original data. As I understand, we can transform the margins using the cumulative distribution function ...
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35 views

Probability with copulas

How can I express the conditional probability $P(X\leq x\mid Y\leq y)$ with copulas? I have seen, in another post, that you can do it, but with $P(X\leq x\mid Y=y).$
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How to add dependence between random vectors using a copula?

I understand that copulas can be used as a tool to add any conceivable dependence to a pair of random variables. However, I would like to add some dependence between two random vectors. Let us ...
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51 views

If margins are normal then why we need to transform to uniform in copula model

I have read many questions about Gaussian and Gaussian copula. I really cannot figure out: when and when not to use Gaussian copula? If the margins are normal then we can use Gaussian to model the ...
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91 views

Parameter estimation using copulas

I am struggling with a pretty basic question in parameter estimation using MLE of Copula ( and its underlying distribution) I have data X, which is independently sampled from a mixture of two ...
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Difference between DCC copula and factor copula models

I'd like to see if I understood this correctly (probably not). Assuming I have a data set $[y_1, \dots y_d]$ of returns and I wish to model their dependence through a copula : DCC-copula (Engle 2002)...
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Copulas - what marginals can I use? (theory)

For my research I am using various copulas and I fit different marginal distributions to my data. I've studied the topic of inter-variable dependency quite a bit, however, I do not recall the ...
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Is it possible to have the same copula for two different joint distributions.

Say, I have two random variables $X$ & $Y$, whose CDF is $F(x,y)$. Similar, I have one more set of random variables $P$ & $Q$, whose CDF is $G(p,q)$. Is it possible that $F$ and $G$ have the ...
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What is the advantage of modelling dependency using Copulas?

I have been trying to understand why modeling dependency using Copulas is widely used - specifically, what are the advantages of using Copulas? Here is my understanding: The marginals of the data ...
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Tail dependence of copula

There are some copula families that are able to deal with upper tail dependence (Gumbel and Joe copula) or lower tail dependence (Clayton). We can also rotate these copulae to have another copula. For ...
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Error or performance measure for quantile regression with vine copula

we set up a d-vine copula with 21 trees and are now looking for an error or performance measure of our model. It is basically quantile regression, but there are no regression coefficients, as used in ...
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Construct joint distribution of $X,Y$ such that $E[X|Y=y,y\geq \bar{y}]$ is piecewise linear

Can one construct a joint density $f(x,y)$ such that the marginal distribution of $Y\sim~U[c,d]$, no restrictions on $X$ (it would be great that $X$ also has uniform distribution) as long as it has ...
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Creating a joint density from two asymmetric uniform marginals

Two RV \begin{split} X_1 & \overset{{i.i.d.}}{\sim}\mathcal{U}[0,1] \\ X_2 &\overset{{i.i.d.}}{\sim}\mathcal{U}[0.3,2.08] \end{split} I need to create a joint pdf from these two. Is copula ...
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How to prove the probability in copula and what does it means

I am learning copula. However, it seems quite hard to understand its theory. I found a useful, but with some unclear statements, post. This post can be accessed from here. the link. I just cannot ...
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Why we must transfer values back to their original values using copula

I am quite new to copula models. The main idea of the copula is based on the Sklar's theorem. In copula models, we first need to transform the data to copula data (standard uniform [0,1]). Then, we ...
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Simulate >2 variables from Gumbel Copula

I'm trying to simulate multiple random variables with different taus from the Gumbel copula. For the normal copula it's pretty simple, eg: ...
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Prove independence by using copula

Suppose that I have multivariate random variable $(x_1,...,x_n)$ whose pdf $f(x_1,...,x_n)$ exist and does not depend on $x_i, 1 \leq i \leq n$. An example is random vector uniformly distributed on a ...
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how to calculate the VaR of an equally weighted portfolio of 2 assets using the copula approach?

The R-code Procedure in the GARCH-EVT-Copula Model estimation? . I have been able to do the following steps in R; 1. Fit GARCH models to each series. 2. Extract standardized returns. 3. Transform ...
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Copula is not unique if the margins in not continuous

The copula is a very interesting tool to describe the dependence structure. However, I read that if the margins are continuous then copula is unique. However, if margins are discrete then copula is ...
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Density of mixture copula [closed]

I understand the idea of copula and its benefits. One main advantage of the copula is it allows to model the margins distributions separately from the dependence structures. The density of bivariate ...
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Simulation algorithm using copulas

Say that I have a bivariate random variable $X=(X_1,X_2)$ with known marginal distributions $F_1$ and $F_2$ and a known covariance matrix $S$. However, I do not know the joint distribution of $(X_1,...
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Model groups of variables and their interactions separately

I want to decompose a multivariate pdf $p(x_1, x_2, x_3)$, where each $x_i$ is a collection of one or more random variables, into its "marginals" $p(x_1), p(x_2), p(x_3)$: $p(x_1, x_2, x_3) = p(x_1)p(...
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Predicting / conditional sampling with Vine Copula

I think I understand the concept of Copulas and how bivariate Copulas as building blocks form a Vine structure. But something I cannot get my head around is predicting with a Vine Copula. This should ...
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Why does pnorm() change the correlation in my multivariate normal sample?

I came across 2 problems that puzzle me while simulating variables for a Monte Carlo simulation, using the rnormalcopula command from the rCopula example. The first one is the one from the title, the ...
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Sampling from mixture copula

Sampling from copula is based on inverse transformation method. However, I would like to understand the sampling algorithm from mixture copula. I really spend a long time to search, however, I could ...