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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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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24 views

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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25 views

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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54 views

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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31 views

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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36 views

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 ...
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Regular Vine Copula Construction

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(...
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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. ...
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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 ...
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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., $C[0,1]^2 \rightarrow [0,1]$. ...
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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 ...
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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 ...
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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 ...
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How to define Autocorrelated Copula?

I want to make a copula between two auto correlated timeseries.Since it would be better for the timeseries not to be auto correlated, was thinking about making ARIMA (Autoregressive Integrated Moving ...
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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 ...
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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 ...
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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\...
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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....
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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, ...
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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.
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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 ...
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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 ...
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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 ...
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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 ...
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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}...
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What is the preferred way to show that a 3-dimensional function is a copula?

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 ...
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What do the joint distributions look like? [duplicate]

I know that if I know the marginal distributions, that's not enough to specify the joint distribution. But obviously it can't be "any" joint distribution, it still needs to respect its marginal ...
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Is this exercise question well-posed? Dependence of marginal normals with correlation $\rho$

An exercise question asks me to find the tail-dependence of $X$ and $Y$, where $\operatorname{Corr}(X, Y) = \rho$, and both $X$ and $Y$ are standard normal variables. The tail-dependence is $$ \lim_{...
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How to calculate conditional probability when only marginals are known?

Say $X, Y$ are standard normals with correlation $\rho$. How do I calculate conditional probabilities such as $P(X \le x \mid Y \le y)$? I don't have any assumptions on their joint distribution, ...
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How to use multidimensional copula to obtain a joint distribution in python?

I am following this blog on how to use copula using python and scipy. From what I can understand, the process is as follows Generate samples from a multivariate distribution with a correlation (in ...
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sampling from multivariate distribution using copula

I'm trying to get a sample from a multivariate distribution which is constructed by copula. this is the steps that i go,is it true? at first i estimate the copula and the marginals then get a sample ...
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1answer
105 views

Does the empirical transformation of the margins will give copula data

I am learning coupla. I read that we need to transform the margins to the uniform distribution in order to get the copula data. Is that correct? Also, I read that to obtain copula data, we can ...
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Why does rank correlation only depend on copula, and not on the margins, if the margins are continuous

I read that for continuous margins, then Rank correlation only depend on copula and not on the margins. However, it is not the case for the non-continuous margins. Is that because the Kendall's tau (...