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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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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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Dynamic Copula Toolbox in MATLAB [on hold]

I am trying to use MATLAB's Dynamic Copula Toolbox v 3.0. I already have my PITs (estimated prior). I have to following code so far: ...
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Copula modeling library: Pycopula [on hold]

I am having an issue with the pycopula library. The example (provided on https://github.com/blent-ai/pycopula) imports a csv ...
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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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Probability Integral Transfroms [on hold]

I am currently trying to find the dependence structure of two market indices (financial time-series) using a Clayton copula. I decided to go for the Two-Step Likelihood Estimation whereby the marginal ...
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Fit a copula model in R [closed]

I want to accomplish the task of creating an optimal portfolio of stocks, the yield between which is modeled using kopulas. And I have data: return of 4 stocks: ...
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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 ...
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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
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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 (...
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Why aren't copulas unique for non-continuous random variables?

I have read from the Sklar's theorem that for continuous random variables, then copula is unique. I really do not understand why? Could someone please explain to me why the copula not unique if the ...
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Copulas with positive likelihood ratio dependence

Let $C(,)$ is an absolutely continuous two dimensional copula. Let the $C_{1}$, $C_{2}$, $C_{12}$ denote the derivatives wrt to the first, second, and mixed variables respectively. We say $C$ is PLR ...
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1answer
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How to generate random variables which are correlated and yet marginally identically distributed? [closed]

I am wondering if there is a process to which we can generate random variables where there is a correlation structure between them, yet they are still marginally identically distributed? One idea that ...
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Why does correlation changes so much when converting data to pseudo observations for copula fitting?

I'm trying to model the joint distribution of time to failure of 2 (in future possibily more than 2) components. So far what I know is the following: The marginals of these components are ...
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Does this copula have a name?

Let \begin{equation} c(u_1,u_2|k) = k\,\big((1-u_1)\,(1-u_2)\big)^{k-1}\, _2F_1\!\left(1-k,1-k;1; \frac{u_1\,u_2}{(1-u_1)\,(1-u_2)}\right) , \end{equation} where $k \in \{1, 2, \ldots\}$ and where $...
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Proof for copula determined by correlation matrix

How can I proof that the copula of an elliptical distribution $El(\mu, \sigma^2, g_n)$ is fully determined by the generator function $g_n$ and the correlation matrix extracted from $\sigma^2$.
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Correct Interpretation of copula contour plots

Going into exploratory data analysis with the intention of fitting copula models, I was looking at the famous copula and they mention here that either contour or 3D ...
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1answer
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Approximation of copulas

I'm studying copulas, finished the Introduction to Copulas by Nelsen. I'm interested in the latest/best known/etc approaches for approximating any Copula, or some families of copulas, so would be ...