# Questions tagged [copula]

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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### variables that are normaly distributed but their joint distribution is not multivariate normal with ρ = 0.5 [duplicate]

can you give me an example or explain me how to find one. It can be with copulas
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### AIC / BIC for Model Seleciton in Copula Model

I'm trying to select the distributional model of 30 marginals (which are restricted to have the same distributional family) in a copula model. However, I therefore get 30 Likelihood/AIC/BIC values for ...
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### Spearman $\rho$ as a function of Pearson $r$

It is common to talk about the linear correlation, Pearson's $r$, between two random variables $\{(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)\}$ as having two components: a) the copula and b) the marginal ...
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### Simulated returns from copulas to use in portfolio allocation

I am currently trying to do some portfolio optimization by reproducing the methodology found in Sahamkhadam, Stephan & Östermark (2018) ("Portfolio optimization based on GARCH-EVT-Copula ...
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### Can you use Kendall's Tau to compute covariance matrix?

I am working with multivariate archimedean copulas, and I am wondering how I can extract a covariance matrix out of them? I can get Kendall's Tau matrix of correlation so I was thinking that maybe I ...
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### How to find joint distribution using copula and NIG(Normal Inverse Gaussian) marginal Distribution in R?

I have a question about finding the joint distribution of marginal NIG distributions using Gaussian Copula. I estimated the parameter NIG using the ...
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### What is the difference of $\Sigma$ esimation of Gaussian Copula based on known CDFs VS unknowns

Recently, I read this web page which explains the Copula package in R. A question occurred to me. Consider a data set $D_{n\times d}$ which $n$ is the number of samples and $d$ is the number of RVs. ...
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### Fitting a multivariate T Copula to three variables in R

I have three variables with correlation coefficient of respectively 0.3; -0.2 and 0.1. I want to fit a T copula but when I use the fitCopula function it gives me a single value for rho, which leads to ...
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### Intuitive explanation of “density generators”?

I was reading through Meucci's Risk and Asset Allocation (2005), when I happened upon the concept of a "density generator", which I have not been able to find good explanations for anywhere online, ...
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### Sampling from skew normal copula

For a project, I wish to draw from multivariate skew normal copulas. Initially I thought my approach was correct, but now I believe it's highly unlikely that it's correct. I've read up about the ...
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### Something like Mahalanobis distance when the copula is not Gaussian

Mahalanobis distance accounts for different variances of the marginal variables and correlations between the marginal variables. However, there is an implicit (maybe explicit) assumption that ...
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### Can skew t-student copula models any types of dependency structures and its benefits over vine models

I read that skew-t copula has been used widely as a multivariate copula model. However, I really do not know whether this function would helpful for other complex dependency structure for example ...
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### mean of copula parameters and the kendall taus over replicated simulation

Suppose that I have a simulation data (1000 repeated). Assume further that I have simulated the data from copula models. Then, I would like to test my algorithm (to estimate the copula parameters). ...
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### Patton's Symmetric Joe-Clayton copula

I am currently trying to apply Patton's Symmetric Joe-Clayton Copula, described in his "Modelling Asymmetric Exchange Rate Dependence". I am currently looking for the closed-form relation (if there is ...
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### Correlated samples from t copula

I want to generate correlated samples from t copula for some data. If I cannot estimate linear correlation parameters and degrees of freedom from copulafit, can I ...
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### Generating large number of correlated variables with copulas

I need to generate a lot of correlated variables (at least $9000$). I have been using Gaussian copula so far and it seems to be working fine. However, Gaussian copula is tail independent which can be ...
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### fitting high dim copula to residuals of a garch model very slow in R [closed]

I'm looking for some help on understanding on the fitting procedure of a normal (or any other for that matter) copula in R. My main goal is to either improve computational speed, or revise my strategy....
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### R: Calculating the convolution of two (multivariate) functions using FFT

I'm looking for a way to calculate: $$(f\ast g)(x) = \int_{\mathbb{R}^d}f(y)g(x-y)dy$$ in R. I have solved this problem using Monte-Carlo integration. However, ...
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### Decomposing a random variable into marginals and copula

I’m having trouble getting understanding how to actual construct a copula, from my understanding it captures the purely joint features of a joint distribution. I’ve been working with the following ...
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### What are properties of copula functions in simple words? [duplicate]

I read a lot about copula functions lately, and I think I understand the basic concept quite well. But I still have trouble understanding this summary of copula properties: Can someone help me to ...
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### Correct C-Vine Configuration to emulate a predefined correlation matrix

I am trying to simulate a vine copula with a predefined dependence structure, so I can generate samples for my desired dependence structure. However, I am having trouble defining the Vine structure ...
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### Probability Integral Transforms (Not getting U(0,1))

I am trying to transform my GARCH standardized residuals to PITs in order to use them in a copula. The following code has been so far applied: ...
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### Why should we study copulas? [closed]

I am new to the study of copulas and I would like that someone could provide some examples where they are applied, their usefulness and so on. Any help is appreciated. Thanks in advance.
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### Trouble with copulas: how do we justify its definition?

A bivariate function $C(u,v)$ that maps $[0,1]^{2}$ to $[0,1]$ is a copula if it satisfies the following two conditions: (i) Boundary conditions: \begin{align*} C(u,0) = 0\\ C(0,v) = 0\\ C(u,1) = u\\ ...
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### Question about using Bayesian rule as a classification for continuous data set

Please note that my question is not about coding. I am now learning Bayesian classification and I think I understand it in a discrete case. I have trouble understanding it for multivariate continuous ...
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### Copula partial derivates

I have some troubles with the demonstration of this theorem: Let C be a copula, for any v in I=[0,1] the partial derivative for u exists for almost (Lebesgue meaning) all u, and it is included between ...
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### Sum of two dependent random variables with copula

I'm trying to calculate sum of 2 random variables by using Copula Theory in R or Matlab. However, I have very limited knowledge about probability. Actually I read a lot of theoretical information ...
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### Using mixture models as a prediction model

I read many papers that used mixture model to predict, for example, The diagnosis of a disease. For example, assume that there are a measurements on different variables for healthy patient and ...
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### Impose copula on two independent random variables [closed]

I want to impose a Gumbel (or Gaussian) copula on two independent random variables ...
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### Is it possible to evaluate similarity (as in Kolmogorov-Smirnov test) between two sample vectors using copulas?

Consider the Two-sample Kolmogorov-Smirnov test: given 2 vectors of samples $X$ and $Y$ it is possible to test whether they are drawn from the same continuous distribution by calling (in R, for ...
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### Statistical prediction model with copula

Copula models are used widely to present the dependency structures among variables. Assume that I have a disease dataset. Assume further that I need to diagnose patients. Suppose that ...
In 3 variables regular vine construction, we have $$f(x_1,x_2,x_3) = \text{marginal}\times\text{unconditional pairs}\times\text{conditional pairs}=f_3(x_3)f_2(x_2)f_1(x_1)\times c_{12}(F_1(x_1),F_2(... 1answer 35 views ### simulation vine copulas I am trying to simulate the following structure: C_{123}(C_{12}(u_1, u_2; \theta_1), u_3; \theta_2) I am able to simulate the inner C_{12}, I do simply use the method of the conditional copulas. ... 0answers 20 views ### Manipulating samples with Extreme Value Theory First of all, i'm an electrical engineer and i know very little about statistics and probability. In one of my work, i'm trying to somehow combine(this word might be wrong..) Extreme Value Theory and ... 0answers 26 views ### How does copula links the margins [duplicate] I am reading about copula. One simple definition of copula is that: Copula joins the uniform uni-variate margins to their multivariate distribution functions, i.e., C[0,1]^2 \rightarrow [0,1]. ... 1answer 56 views ### Find a copulas given joint distribution We were given some homework to complete and would like to know how do you calculate the copulas I know from the definition that: C(X,Y)=FX,Y(Fx^-1, Fy^-1) and ill have to find the marginals by ... 0answers 20 views ### fit a gumbel copula to 500 set generated random number i have a question, of finding the tail coefficient of gumbel copula. I generated 500 set of random variable, with 4 different theta of 1, 1.5, 2 and 3. Then I fit them to gumbel copula with maximum ... 0answers 24 views ### Copula-based joint models with the same covariates for the marginals? I'm estimating a copula-based joint multinomial logit - linear regression model. The utility structure of the multinomial logit model is represented by u_{ij}*=\beta_j'x_{ij}+\epsilon_{ij}. In the ... 0answers 25 views ### Bounds on quantiles of the minimum of summations of (possibly dependent) random variables Suppose I have 2N continuous random variables X_1, \ldots, X_N, Y_1, \ldots, Y_N and that I can evaluate the quantiles of the respective distributions. Given a value w \in [0, 1] I would like to ... 0answers 33 views ### Gaussian Copula: Transformation to Normality and Interpretation of Copula Correlation Assume we have the marginal distributions for two variables: Security1_Price and Security2_Price. These two distributions are mapped to standard normal distributions U1 and U2. How exactly does this ... 0answers 13 views ### Frank copula with no dependence From Wikipedia, the Frank copula is the function C(u, v) such that:$$C(u, v) = \frac{1}{\theta} \log\!\left[ 1+\frac{(\exp(-\theta u)-1)(\exp(-\theta v)-1)}{\exp(-\theta)-1} \right]$$for \theta\... 1answer 32 views ### differences between conditional probability and dependency Sometimes, I read articles about conditional probabilities and other articles about conditional dependency. My question what is the main differences between them? For example, "https://en.wikipedia.... 0answers 17 views ### what does non-nested copulas mean? I read from "Pair-copula constructions of multiple dependence", the following statement: "The likelihood of the Clayton copula is lower than that of the Student copula (39.72 vs. 47.81). However, ... 0answers 18 views ### How is this copula relation derived? In the first answer to this question: Why is Gaussian Copula's Tail Dependence Zero? it says: Where does the second equality come from? It doesn't seem clear to me at all. 0answers 21 views ### Fitting wrong copula type to a real data set I have developed a new mixture copula model. This model overcomes some limitation of copula models. I tested my new model on a simulation data. The model shows a superior result. My supervisor asked ... 2answers 332 views ### Quantifying dependence of Cauchy random variables Given two Cauchy random variables \theta_1 \sim \mathrm{Cauchy}(x_0^{(1)}, \gamma^{(1)}) and \theta_2 \sim \mathrm{Cauchy}(x_0^{(2)}, \gamma^{(2)}). That are not independent. The dependence ... 0answers 25 views ### correlation measure in copula I'm reading about copula but I'm a bit confused about it: we know that the Gaussian copula pdf is equal to :$$C (u_1, u_2, u_3,…, u_n; Σ) = |Σ|^{-1/2} \exp (-1/2 ε^{T}(Σ^{-1} – I)ε)$$where Σ is ... 0answers 41 views ### Best way to model the dependency of these two random variables (copula?) I'm modelling the joint PDF of two variables that looks like this , where vt and vr are the random variables. The dashed line shows the joint pdf assuming they are independent (the product of its ... 1answer 67 views ### Finding expression of n-th derivative, when n is large For completeness, assume C is an Archimedean copula with some generator function \varphi, which is usually assumed to have nice properties. It is known that$$ C(u_1, u_2, \ldots, u_n)=\varphi^{-1}...
I am currently working with 3 dimensions, and have some functions $C(u_1, u_2, u_3)$ for which I need to check whether or not they are a copula. What are all the requirements that I need to check? In ...