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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Error message when fitting 3-dimensional Copula [migrated]

I want to use a Gumbel Copula for a 3-dimensional data set. I use R and the Copula package. It gives me an error, though. This ...
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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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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?

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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69 views

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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59 views

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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29 views

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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137 views

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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215 views

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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167 views

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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43 views

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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260 views

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 ...
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Is the Gaussian copula (for d=2) with normal margins identical to the bivariate normal?

I am not sure about this: In the 2 dimensional case, if I consider the Gaussian copula, is this identical to the bivariate normal distribution, in the case I choose the normal distribution for the ...
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141 views

Questions concerning copulas

I am new to the topic of copulas and my math is limited. I have different questions: 1. Is it correct to say, that $C: [0,1]^d \rightarrow [0,1]$ is a mapping from a multidimensional distribution to ...
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Method for generating correlated non-normal data

I'm interested in finding out a method for generating correlated, non-normal data. So ideally some sort of distribution that takes in a covariance (or correlation) matrix as a parameter and generates ...
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756 views

Difference between multivariate standard normal distribution and Gaussian copula

I wonder what the difference between multivariate standard normal distribution and Gaussian copula is since when I look at the density function they seem the same to me. My issue is why the Gaussian ...
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Problem with the formulation of a gaussian copula likelihood function

I recently got to hear about copulas which to me sounded like a nice tool to model relationships between variables. I decided to try to implement the likelihood function for a bivariate Gaussian ...
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224 views

How to simulate a hidden Markov chain?

I want to simulate data from a 3-state hidden Markov chain with a known matrix of transition probabilities. Each state corresponds to a bivariate data with known marginals that the dependence between ...
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78 views

What is the Cauchy meta distribution?

I overhead a professor speak about the Cauchy meta-distribution, but I am unable to find anything about it on the web. My question is what is the Cauchy meta distribution and what is the theory behind ...
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Why Copula need i.i.d assumption for marginal distribution?

Does anyone know that are there some assumptions for Copula method. I heard from someone that The data should be i.i.d (independent and identically distributed). Let's say. If I want to capture the ...
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117 views

Generating time series with copula

I want to generate univariate time series in R using copulas. Let $X_1, X_2, \ldots X_N,\ldots$ denote random variables such that joint distribution of $X_t$ and $X_{t-1}$ is $C(F(X_t), F(X_{t-1}))$, ...
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238 views

Joint Relationships between log normal variables and their Gaussian counter parts

I am wondering if two dependent log normal variables $X$ and $Y$ are jointly log-normal would there Gaussian counter parts as in $\ln X$ and $\ln Y$ be jointly normal ? Also what about the converse as ...
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How do I prepare data which has a trend for use in a Copula model?

I want to use a set of daily water quality data including 3 parameters in a Copula model. Somebody told me these data do not have a condition of a random variable to use in copula, and I should do ...
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Deriving conditional distribution using Gaussian copula

This question shows how to derive an analytical expression for the conditional distribution from a multivariate normal. I am curious how well this extends to when there's a Gaussian copula, but ...
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Upper bounds for the copula density?

The Fréchet–Hoeffding upper bound applies to the copula distribution function and it is given by $$C(u_1,...,u_d)\leq \min\{u_1,..,u_d\}.$$ Is there a similar (in the sense that it depends on the ...
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269 views

Is there a multivariate version of the Weibull distribution?

I hope this one is self-explanatory, but let me know if something is unclear: Is there a multivariate version of the Weibull distribution?
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216 views

Farlie-Gumbel-Morgenstern Bivariate Gamma Distirbution

Given the variables $X$ and $Y$, which are correlated, $X\ge0$, $Y\ge0$ and each follow a gamma distribution with different shape parameters, i.e.,$X\sim Gamma(a_1,\alpha)$ and $Y\sim ...
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262 views

Generating samples of correlated normally distributed variables with some of the variables pre-selected

I would greatly appreciate any of you who could help me with this challenge. I am going to state the problem in sequential order, so as to make it clear: I have $n$ normally distributed random ...
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388 views

Attainable correlations for lognormal random variables

Consider the lognormal random variables $X_1$ and $X_2$ with $\log(X_1)\sim \mathcal{N}(0,1)$, and $\log(X_2)\sim \mathcal{N}(0,\sigma^2)$. I'm trying to calculate $\rho_{\max}$ and $\rho_{\min}$ for ...
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228 views

Joint probability and Gaussian copula

I have $\Pr(A)=29\%$ and $\Pr(B)=10\%$, where $A$ and $B$ are two events which are not independent. In fact, a correlation measure suggests they're correlated by $\rho=0.8$. I would like to ...
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Fitting copula for discrete margins

How can I fit a copula for a bivariate vector of negative binomial and Bernoulli margins? I would prefer a Frank or Clayton copula.
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173 views

Joint distribution of two sums of correlated variables

Suppose that $(X_1, Y_1)$ and $(X_2, Y_2)$ are independent and have the same joint distribution $F_{X,Y}$, which is a known copula $C_{X,Y}(F(X), F(Y))$. Also, suppose that $V = X_1 + X_2$ and $W = ...
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Had statisticians predicted 2008 financial crisis?

Are there any statistical or econometric studies before 2008 that predicted 2008 financial crisis? Note that there are some publications that attemp to predict contagion between markets using copula ...
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Introductory reading on Copulas

For some time now, I have been looking for a good introductory reading on Copulas for my seminar. I am finding lots of material that talk about theoretical aspects, which is good, but before I move ...
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744 views

How to simulate from a Gaussian copula?

Suppose that I have two univariate marginal distributions, say $F$ and $G$, which I can simulate from. Now, construct their joint distribution using a Gaussian copula, denoted $C(F,G;\Sigma)$. All the ...
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Dependent thinning Poisson process

If $N_1$ and $N_2$ are independent Poisson processes then the superposition is a Poisson process. Is it possible to construct two dependent Poisson processes such that the superposition is a Poisson ...
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Estimating joint distributions using copula package in R

I am trying to estimate the joint distribution of stock returns using the copula package. I have read a couple of papers on copulae, but alas my lack of math ...
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Copula with 4 Poisson and 1 Bernoulli margins in R

I want to joint 4 Poisson variables and 1 Bernoulli variable with D-vine copula. How can I do this with R?
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954 views

What are some techniques for sampling two correlated random variables?

What are some techniques for sampling two correlated random variables: if their probability distributions are parameterized (e.g., log-normal) if they have non-parametric distributions. The data ...