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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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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39 views

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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53 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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42 views

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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25 views

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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65 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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59 views

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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25 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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46 views

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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46 views

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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234 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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1answer
134 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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51 views

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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1answer
62 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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142 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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55 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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107 views

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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296 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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296 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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217 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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105 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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317 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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106 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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160 views

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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1answer
157 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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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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391 views

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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249 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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85 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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126 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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261 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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103 views

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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297 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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250 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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302 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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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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250 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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186 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 ...