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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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How to predict using a copula approach?

I have a dataset with both continuous and discrete variables the target variable is 0-1 and I was wandering on how to predict the target var with the copula regression. I'm using python to do so and I ...
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Simulate Gaussian copula with negative pair-wise correlations

I am now trying to simulate a multidimensional (let's say 4 dimensions) Gaussian copula. Given software restrictions, I can only use Excel for this simulation. That is why I am trying to implement the ...
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How to prove this relation for Kendall's distribution function (or Kendall's measure)

Kendall Distribution Function (Nelsen, 2006, p. 163) Or Kendall Measure (Salvadori et al., 2007, p. 148) Or Kendall Function (Joe, 2014, pp. 419–422) is the cumulative distribution function (CDF) of ...
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Steps for Forecasting with known copula's parameters

I want to calculate the Mean absolute percentage error (MAPE) for my copula model. I am stuck at the forecasting step. I am not specifying the copula here for different data pairs. I have two time ...
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Joint distribution of the variables [closed]

I want to use the copula to model the joint distribution of precipitation and stream flow data for multivariate drought analysis. I have determined the marginal distributions for the variables. How ...
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How many degrees of freedom in a T-copula is commonly used to model financial data?

I'm looking to fit some T-copulas to my financial return data. Unfortunately, the software I'm using can only fit a T-copula with a fixed degree of freedom parameter. So what parameter should I use? ...
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Suppose $(X,Y)$ have copula $C(u,v)$, does $(aX,aY)$ have the same copula for $a>0$?

Suppose $(X,Y)$ have copula $c(u,v)$ in the sense of $Pr(X\leq x,Y\leq y)=Pr(F_X(X)\leq F_X(x),F_Y(Y)\leq F_Y(y))=Pr(U\leq u, V\leq v)=c(u,v)$, where $u\equiv F_X(x)$ and $v\equiv F_Y(y)$ and $c(u,v)$ ...
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Should I not use copula if there is no significant dependence?

I have two variables, and I would like to get the joint distribution of those. I want to use copulas for that. However, when I checked for the dependence between those, I found no significant ...
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What is the formula for the conditional inverse function for the Ali-Mikhail-Haq and the Farlie-Gumbel-Morgenstern Copulas?

I am trying to do a Monte Carlo simulation and want to define a function for the conditional inverse function for the the Ali-Mikhail-Haq and the Farlie-Gumbel-Morgenstern Copula. Here is an example ...
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Correlation of a Gaussian copula

Suppose I have a 2D Gaussian copula with correlation matrix $$ R = \begin{bmatrix} 1 & \rho \\ \rho & 1 \end{bmatrix} $$ for $\rho\in[-1,1]$. The Copula is $$ C_R(u)=\Phi_R\big(\Phi^{-1}(u_1),\...
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How to calibrate and simulate a copula-garch model in R using rmgarch package

So I have been trying to calibrate and simulate cryptocurrencies for VaR and ES analysis using the rmgarch package in R. I have been using the t-copula, my reason being that cryptocurrencies' ...
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How to write a function for the normal copula in R?

How can I write the following function for the normal copula in R? $$ C_\theta(u, v)=\Phi_\theta\left(\Phi^{-1}(u), \Phi^{-1}(v)\right), $$ where $\Phi$ is the $N(0,1)$ cdf, $\Phi^{-1}$ is the ...
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Return period of vine copula

In the formula for "OR" joint return period of 3-dimensional copula modeling, we need to find C(u,v,w) but when we model using vine, we are only able to obtain the copula C(uv|w). So, how to ...
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What are the convincing examples of copulas uncovering not obvious statistical dependences (or the lack of them)?

What may be a good, strong and convincing example demonstrating the power of copulas by uncovering some not obvious statistical dependencies? I am especially interested in the example contrasting ...
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Expression of estimated standart deviation in GAMLSS model

I'm trying to replicate the results of the North Carolina Birth Data Analysis in the paper A Bivariate Copula Additive Model for Location, Scale and Shape by Giamperro Marra and Rosalba Radice (https:/...
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Grid search for estimation of degrees of freedom parameters in likelihood function

In the script below I attempt to estimate parameters for Apple and Amazon using a Gaussian Copula with t-Student marginals for the purpose of this exercice. When executing the script, I notice at each ...
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Endogeneity Analysis without the access of raw data?

I currently have the correlation/covariance matrix for a set of variables, as well as the output from a regression analysis, but lack access to the underlying raw dataset. Given these constraints, ...
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How are the joint distribution and dependency related? [closed]

Here are some notes about copula functions, Copula is a probability model that represents a multivariate uniform distribution, which examines the association or dependence between many variables. Put ...
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More than one possibility for the generator function of a Clayton's copula?

This question is about the bivariate family of Clayton's copulas, defined as: $$ C(u,v)=\left(u^{-\theta} + v^{-\theta}\right)^{-1/\theta} \; \text{,} \quad \quad \text{(1)} $$ with $\theta \in [-1, +\...
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Fitting a Copula from Scratch

I am trying to learn about how to work with Copulas. I find that I am often getting lost in the notations and distributions, and wanted to try and solidify my understanding. As it stands, here is my ...
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How to draw samples from two correlated Negative Binomial variables?

Data and problem description: my data is the number of corner kicks of home team, away team, total corner kicks and corner kicks difference. Below is code for data and the plots (assuming the number ...
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Advantages of using Vine Copulas over Regular Copulas?

I am new to Copulas and am trying to conceptually understand that differences between the two main types of Copulas: Regular Copulas and Vine Copulas. Both are used to simulate data from correlated ...
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best strategy to test bivariate data

Here's a revised version of your text: I have two sets of data: Intensity and Duration. For each set, I possess both observation data and model data, denoted as (I_obs, I_mod) and (D_obs, D_mod) ...
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Generate samples from multivariate correlated data which have non-parametric cumulative distribution functions

I have 40 samples that contain information about 6 variables (hence a 40x6 data matrix). Each variable (column) has a cumulative distribution function (marginal distribution) based on the 40 values, ...
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Parametric copulas with marginals that are regressions

In Dependence Modeling with Copulas (Harry Joe) I'm struggling to interpret the meaning of a statement. In Chaper 5.1, it is stated: Parametric inference for copulas For dependence modeling with ...
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What is this copula?

I have a bivariate sample in the [0,1] square for which I am trying to find the copula that best describes it. (I am new to copulas.) So far, I have tried all classes in the "copula" R ...
dganghel's user avatar
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Copula to ensure one team wins and the other loses (Bernoulli margins)

Team $1$ has a historical win percentage of $p_1$. Team $2$ has a historical win percentage of $p_2$. The upcoming game features team $1$ against team $2$ and cannot end in a tie (one team wins, and ...
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Are precipitation and soil moisture time-independent variables?

I was studying about Copula functions from here. It says: Basically, copula is a set of mathematical tools that have the ability to connect two or more time-independent variables (Nelsen, $2003$) As ...
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Are there margins such that, while the "correlation" parameters of a Gaussian copula are positive, the correlations between the margins are negative?

Let there be a multivariate distribution $F$ with margins $F_1,\dots,F_n$ and a Gaussian copula with "correlation" matrix $\Sigma$. Let the off-diagonal elements of $\sigma$ be positive. Let ...
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Is it possible to sample a copula in the original units?

I have a fairly high dimensional dataset that is not mvnormal. I used a copula to model the data and it fits well. How can I go about generating random samples from that copula that are in the ...
user111024's user avatar
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Transforming data with a fitted distribution function

I have a bivariate dataset on $[0,1]^2$ in which I am interested in fitting a joint distribution. I fit a Gaussian copula but am unsure how to judge if it's a good fit. I tried transforming my data ...
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Nonparametric test (akin to a sign test?) for multiple interacting effects across multiple conditions

Problem I have $K$ sets of conditions (index by $k\in\{1,..,K\}$), and each set has $N_k$ conditions. For example, if $K=2$ and $N_1=N_2=2$, we could call the conditions (A,B) and (C,D). I have ...
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Estimate multivariate distribution with several variables on real data (continuous and categoricals) and sample from it

I have a complex dataset, collected through a survey, with both continuous (such as Age, Body mass index, etc..) and categorical variables (i.e. Gender, Education, etc..). I want to estimate their ...
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How to calculate the covariance-standardized residuals from a joint distribution estimated with the copula density function

I have issues when reading a paper when calculating the eta parameter in the following equation where the authors of the paper describe eta as the vector of the covariance-standardized residuals, ...
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What is the difference between copulas and normalizing flows?

The goal of normalizing flows is to produce arbitrarily complex probability-distributions from a simple distribution (usually the Normal distribution) through learning an invertible transform. Copulas ...
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Does an algorithm exist that generate copula when marginal distributions are available and stable distributed and correlation is not simple?

I have simulated data of a 4-dimensional random variable $(X_1,X_2,X_3,X_4)$. The individual pdfs of these random variables, i.e., $X_i$ where $i\in\{1,2,3,4\}$ turns out to be stable distributed with ...
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copula and categorical data transformation

I plan to model copulas with data that has categorical variables. Copula modeling with categorical variables requires a transformation of categorical variables into continuous (link: https://hal....
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Differentiating a copula joint distribution

I am trying to derive the differentiation of joint copula from this paper http://www.nicksun.fun/assets/ms_references/madsen2009.pdf, which is done in equation (4.3). To summarize I fail to ...
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Using Copulas to find mutual information

I have two multidimensional datasets $X, Y$ of dimensions $m \times n$. Here $m$ is the successive measurements and $n$ is the data collected during each measurement. We can say each of $m$ are ...
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Are two marginal distributions of a student-t copula equivalent to using two independent uniform distributions?

I am trying to figure out if these two are the same: Using the marginal uniform distributions of a student-t copula Using independent uniform distributions I have generated SAS code to figure this ...
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Conditional CDF given one dimension equals derivative of joint CDF towards that dimension divided by the density at that dimension?

So I am familiar with the following: $$P\left(X<x|Y=y\right) =\int_{-\infty}^{x}f\left(X=u|Y=y\right)du=\frac{1}{f\left(Y=y\right)}\cdot\int_{-\infty}^{x}f\left(X=u,Y=y\right)du$$ But during a ...
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Should the data transformation to the uniform [0,1] always be performed in copula modeling, even for Archimedean copula families?

Is the data transformation to the uniform [0,1] always required in copula modeling, even for Archimedean copula? I have read some sources stating that the first step in copula modeling involves ...
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Uniqueness of a Latent Representation Under Monotonicity Condition?

Suppose that I observe a bi-variate joint distribution over two random variables, $(X_1,X_2)$. I want to represent this joint distribution as arising from a function $F$ applied to i.i.d. uniform ...
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Fitting Vine Copula tree by tree

I am using the R programming language. I want to manually fit the D-vine copula for tree level 2 using BiCopHfunc(). Still, I ...
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Interpretation of basis functions in a logistic regression: can we test for univariate and multivariate/copula differences between the categories?

O'Brien (1988) has shown that a strong method for doing multivariate testing is to reverse the problem. That is, instead of seeing if the category impacts the measured values, see how the measured ...
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Are there families of known parametric copulas for non-standard marginal normal distributions?

I know that a family of Gaussian copulas generates a standard bivariate normal distribution if and only if the marginal ones are standard normal. This characterizes the Gaussian copulas, where I have ...
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Generate nonnegative variates with mean 1 and specified variance-covariance

Problem In several applications in surveys, it would be helpful to be able to generate a set of $R$ $n$-dimensional variates with the following properties: Has mean vector $1$ Has a specified ...
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statistics linking McFadden's $R^2$ to the relationship between two binary variables, akin to correlation (Copula with Bernoulli margins?)

My goal is to create a visualization of the strength of the McFadden's $R^2$ of a (multinomial) logistic regression, where McFadden's $R^2$ is $1-\dfrac{LL(M_1)}{LL(M_0)}$, involving the ratio of the ...
Dave's user avatar
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Calculating conditional probability using VineCopula in R

I have a dataframe X (with columns x1 and x2) and would like to calculate conditional probability, something like P(x1<0.5|x2&...
lsr729's user avatar
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Uniqueness of copula when marginals are continuous

I have a basic question about copula. I am not an expert in statistics myself but use statistics for modelling and data analysis a lot. I have read in multiple sources and also in Wikipedia that: ...
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