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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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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66 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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73 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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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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328 views

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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153 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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70 views

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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184 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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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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119 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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122 views

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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329 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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107 views

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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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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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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253 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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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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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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271 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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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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261 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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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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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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252 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.