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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Copula density bounds

I was wondering if someone can help me with a problem I encountered in my work. I need a bivariate copula density that meets two constraints at the bounds, and I have difficulties in finding one that ...
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How do we separate marginals from dependence using copulas, and why do we assume uniform marginals?

I read that one advantage of using copula function is that, we can separate the marginals from dependence between variables. I tried to understand how we can do that but I could not find the answer. ...
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Partial Derivative of Joint Distribution Function interpretation

Suppose we have \begin{equation} F(x,y) = \int_{-\infty}^x \int_{-\infty}^y f(a,b) \ db \ da \end{equation} From this, we can say the following: \begin{align} \frac{\partial F(x,y)}{\partial x} ...
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Empirical multivariate probability integral transform

Is there a 'simple' way to obtain a non-parametric empirical multivariate probability integral transform? Univariate case The probability integral transform relates to the transform of any random ...
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Joint Probability Density Function

I'm trying to find the Joint Probability Density Function of three variables, they are random continuous variables. I was thinking about using a copula function since I saw them recommended here ...
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39 views

Simulate a Gaussian Copula with t margins

The task is the following: Given is $Z_1,...Z_{50}$ different hypothetical assets. Each $Z_k \sim t_3$ with standard deviation $\sigma=0.01$ and $\tau(Z_i,Z_k)=0.4$ for $j\neq k$. I want to ...
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36 views

Simulation of the cdf with copulas [duplicate]

Is this a proper way to simulate the joint cdf of normal rvs with perfect positive correlation? I followed these steps: I generate 10 000 observations for two independent uniform rvs, $U_1\sim ...
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34 views

Copula vs conditional distribution

Let $\xi_1,\xi_2$ be two real-valued random variables with joint distribution $P$. The latter gives us marginals $p_1,p_2$ conditional distribution $p_{12},p_{21}$ and the copula $C$. The latter ...
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What does a copula density explain about dependence of random variables?

I am studying copulas and I find it difficult to understand what a copula density tells me about the dependence of random variables. For example, if I have a Gaussian copula density, what can I say ...
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40 views

Appropriate number of degrees of freedom in t-Copula

In a consultation paper (EBA/CP/2014/08) the European Banking Authority (EBA) wrote: “it is proposed […] that Gaussian or Normal like Copulas are not to be used for operational risk modelling. For ...
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34 views

Simple Student Copula simulation

I want to simulate a t copula with given correlation parameter $\Sigma$ and $k$ degrees of freedom. I can't find any literature about practical simulation, so I am trying new approaches. (I also have ...
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showing that a function is a copula

In general, is there an easier way of showing that a function is a copula than showing that: $C(u_1,\dots,u_d) =P(U_1\le u_1,\dots,U_d \le u_d) \quad$is nondecreasing in each $u_i \in [0,1] $ ...
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67 views

Does principal components analysis lose any information regarding the interdependence of the variables?

I have often heard that a copula describes in full the interdependence of a set a random variables. Lets say I want to generate a set of random variables that conform to an observed joint probability ...
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132 views

Dependent identically distributed random variables

If $X_1$ and $X_2$ are dependent identically distributed, can we show that $Pr(X_1>X_2) = Pr(X_2>X_1)$? For i.i.d, it is obvious, but what if they are dependent?
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survival function in terms of copula

Is the survival copula the equivalent of the multivariate survival function? In other words, can I write $\bar{C}(u,v) = S(u,v) = u+v-1+C(1-u,1-v) $ where $\bar{C}$ is the survival copula, $S$ the ...
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1answer
39 views

How to choose what copula to use for a certain application?

I'm using the copula package in R for modelling dependece using copulas. 1)What is the suggested course of action for choosing a copula model? 2)Should I use the function ...
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310 views

Farlie-Gumbel-Morgenstern copula

I have the Farlie-Gumbel-Morgenstern copula and I want to generate two gamma marginals and find an expression for the linear correlation. I understand that to get the random variates $(u,v)$ I need to ...
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42 views

Copula Calibration

I've developed a step by step procedure for estimating a copula based upon 2 stock time series returns but I don't understand and have not implemented one step that is discussed in most of the copula ...
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linear correlation formula and maximum using Copulas

I am currently working on linear correlation between two random variables functions (say cdf $F$ and $G$). As far as I understand it is possible to correlate those random variables with copulas. For ...
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104 views

Simulating from empirical copula density estimate

I went through these excellent slides by Prof. Arthur Charpentier on the use of Kernel density estimators (KDEs) with boundary correction to estimate Copulas in a nonparametric fashion. As explained ...
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Measuring dependence of variables with measurement errors and copulas

The weight of 100 subjects is measured twice resulting in the normally distributed $X_1\sim N(\mu_1,\sigma_1)$ and $X_2\sim N(\mu_2,\sigma_2) $. I am interested in the correlation between the ...
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35 views

Analytical Formula for Exceedance Correlation of Multivariate Normal Distribution and others

I understand that the Exceedance Correlation concept. Knowing that the multivariate normal distribution has asymptotic independence on the tail, lower and lower exceedance correlation approaching to 0 ...
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43 views

Help understanding copula version of Spearman rank correlation

I'm reading through this article (http://www.sciencedirect.com/science/article/pii/S0047259X06000662) where they have a population version of the Spearman rank correlation. I'm having a little bit of ...
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25 views

Why is sklar's theorem written for bivariate case only?

I read An Introduction to Copulas by Nelsen. Just wonder, Why is sklar's theorem written for bivariate case only?
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How do I implement a copula to transform a multivariate normal distribution to handle dichotomous variables?

I have a bivariate normal distribution where both dependent variables are dichomotous. I can estimate this fine in R using the multivariate normal distribution, but how can I implement a copula to ...
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36 views

How to efficiently simulate values from a multivariate normal given one of the components?

Suppose $X, Y_i$ for $i=1...n$ are standard normal variable but are also correlated so collectively they come from a multivariate normal distribution. Now the complication is what if I want to ...
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How to find copula-based conditional probability P(U|V>=v)?

Using the Copula operator $C$, which for any (possibly dependent) RVs $U$ and $V$ represents the joint cumulative DF of their inverse probability transform. That is, $U^* = F^{-1}_U (U) \sim ...
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44 views

Spearman's correlation as a parameter

Spearman's rank correlation for a bivariate sample $\{ (x_1, y_1), (x_2, y_2) , \ldots , (x_n, y_n) \}$ is generally defined as the correlation between the ranks of the observations, but what is the ...
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38 views

Fitting a Copula to Two Stochastically Dependent Variables in R

I have two sets of observed data, and I would like to model their joint distribution using a copula in R. I have transformed each set into a uniform distribution using their CDFs, and so now I have ...
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48 views

Comonotonic and Countermonotonic RV's and their relation to Frechet Hoeffding Bounds

If $F_1 ... F_d$ are are all continuous, and $X_j \sim F_j$, $j= 1...d$, then the Frechet upper bound corresponds to comonotonic random variables with $$ X_j = F^{-1}_j(F_1(X_1)) \ \ \ \ \ \ \ \ [1] ...
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92 views

Simulating random variables given partial distributions and correlation

After Monte Carlo simulations I obtained approximated distributions for X and Y. Now I want to add some form of correlation between them. To simulate random variables from a distribution the idea is ...
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75 views

Copula density function

In the equation $h_t(x,y|...) = ...$, can anyone explain me why the first derivatives of the marginal distributions are included? $H_t$ is a distribution function and $h_t$ its density function. ...
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Assessing dependencies

I am looking for a method to assess the dependencies between random variables (cross sectional data). I know that I can use copulas models, but I'd like to see if there are any other alternatives.
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What is the equivalent for cdfs of MCMC for pdfs?

In conjunction with a Cross Validated question on simulating from a specific copula, that is, a multivariate cdf $C(u_1,\ldots,u_k)$ defined on $[0,1]^k$, I started wondering about the larger picture, ...
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36 views

Issues with derivative of a copula density

Suppose I have a bivariate copula density with marginals $F(X)$ ($F(X)$ is normal with parameters $\mu_1$, $\sigma_1^2$) and $G(Y)$ ($G(Y)$ is normal with parameters $\mu_2$ and $\sigma_2^2$). I want ...
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73 views

How to simulate from a log-copula function?

Does anybody know how to simulate from a log-copula function? I'm trying to simulate $(u,v)$ from a log-copula function with the CDF: $$ C(u,v, a) = \exp\bigg(1-\big[(1 - \ln u)^a + (1 - \ln v)^a - ...
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Bayesian inference on default probabilities

I have a doubt, I don't have great experience in Bayesian inference and I wondered if it is possible to construct the following model: I'm interesting in copula-dependent probabilities of default ...
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Why BiCopDeriv function in VineCopula package creates NaNs/Inf?

My question is why BiCopDeriv and BiCopDeriv2 function in Vine Copula package of R which produces first and second derivatives of copula density produce NaNs/Inf in this example. Attached is the code. ...
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Using Gaussian copulas to address endogeneity

I am trying to replicate the paper of Park and Gupta (2012) that handle endogeneity using Gaussian copulas - they are basically modelling the correlation between the regressor and the error. Here is ...
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72 views

Can I use SAS Copula procedure or Matlab copulafit to fit count data (Poisson or Negative Binomial)

I want to simulate data (x,y) with dependency using copula. Matlab has the function for t copula, Clayton, Frank, and Gumbel bivariate Archimedean copulas. But I am not sure if these functions could ...
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179 views

Generating random variables from copula function at a given joint probability?

I have one copula function, let's say a 2 dimensional Normal Copula with parameter of 0.5. I want to generate random variable pairs at given copula probability (e.g. 0.9). How can I do that? (since ...
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40 views

modelling a data-set using copula

I have a data set and I transform the data set in to matrix within range [0,1]. https://drive.google.com/file/d/0B6wp1DiHTjBBOXJoc1JhRG5VSHM/view?usp=sharing Can anyone explain the steps in ...
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118 views

Copula for multivariate distributions

Is anyone know how to join two multivariate distributions using copulas in r. For example let $X=f(x_1,x_2, \ldots,x_n)$, $Y=f(y_1,y_2,\ldots,y_n)$ I need to find a copula for joining $X$ and $Y$ ...
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49 views

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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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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197 views

How to obtain real observation from simulated pseudo observation? (from the copula) [duplicate]

I have fitted a normal copula to my data in R using the copula package and generated pseudo observations in the unit square [0,1]^2. I am having trouble retrieving the simulated values: how can I get ...