All Questions
Tagged with density-function copula
24 questions
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Copula density estimation and plotting using orthogonal Legendre polynomials
I have been unsuccessfully trying to replicate a copula density plot based on the following steps:
Use a uniform measure on I=[0,1]
Use an orthonormal basis of shifted Legendre polynomials with the ...
user1531131
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164
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derivatives and distribution of a 3-dimensional copula in R
I am looking for a way to calculate in the R software, the distribution, the density and the derivatives (of order 1, 2) partial of a Gaussian copula of dimension 3.
Indeed, I have three variables (u1,...
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1
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71
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What does evalue the density of a fitted model at specific points mean?
I have read a description of R package and find the following:
"Evaluate the density of the fitted model at (2.747, 0.1467, 0.13, 0.05334)".
I do not understand what the author mean by ...
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What are examples of symmetric copulas $f(x,y)=f(y,x)$ having relative minima for $f(x,x)$?
In a previous posting on this site RepulsiveBehavior I attempted to detail
a quantum-information-theoretic separability/entanglement problem I am pursuing. Detailed issues of sampling sizes for a data ...
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Intuition behind the inverse of the copula density $\frac{1}{c(u,v)}$
If the inverse of a probability $\frac{1}{p(x)}$ represents the unpredictability or surprisal of a sample from random variable $X$,
then what is the intuition behind the point-wise inverse of the ...
- 4,049
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1
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145
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Do copula describe multivariate distributions more accurately than their moments?
Moments approach:
A common way to characterize and describe the density (pdf) of a random variable is to only look at the mean and standard deviation ($\mu_1$, $\sigma_1$) of its pdf. This mentality ...
- 4,049
4
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2
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373
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What is the copula of a variable with itself?
In Sklar's theorem for joint probability functions,
$$f(x,y) = c(F_X(x), F_Y(y)) \cdot f(x) f(y)$$
the copula is $c(\cdot)$ of variables $X$ and $Y$, while $f(\cdot)$ are their marginal distributions.
...
- 4,049
7
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330
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Expressing a marginal probability using copulas
Please correct me if I am wrong and kindly provide me with the correct notations. I have two questions:
We know that for the variables $(X,Y,Z)\in \mathbb{R}^3$, the marginal joint density $f(x,y)$ ...
- 1,226
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If I want to model a bivariate distribution that is symmetric about (0,0) using copula, what copulas can I use?
If I want to model bivariate data $\{X_i,Y_i\}_{i=1}^{n}$ using copula. The true joint density of $(X,Y)$ denoted as $f_{XY}(,)$ is unknown, but I know it's symmetric about (0,0) in the sense that
$f_{...
- 3,050
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Why copula based on CDF instead of PDF
I do understand the mathematic behind probability density function( PDF) and cumulative distribution function (CDF). My problem starts when I try to understand why copula relies on CDF and not on PDF. ...
- 1,680
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Normalizing the joint probability density
I computed the kernel estimators for the copula density for two random variables using:
library(kdecopula)
kde.fit <- kdecop(u)
As the values of density can be greater than one I was wondering ...
- 97
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2
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254
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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, ...
- 662
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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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3
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1
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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}...
- 672
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333
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Finding probability of a point using bivariate copula density
I have a data in the form $\textbf{N} \times 2$. I am using bivariate copula to model the joint density of this distribution. Firstly, I fit 2 marginal distributions independently on each column of ...
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Constructing a joint distribution from pairwise bivariate marginal distributions?
It's fairly well-known that given univariate distribution functions $F_X, F_Y, F_Z$, one can construct the joint distribution $F_{(X, Y, Z)}(x, y, z) = C(F_{X}(x), F_{Y}(y), F_{Z}(z))$, where $C$ is ...
- 385
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296
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Find PDF and CDF for bivariate distribution in R
I have a bivariate data with A=log-logistic B=weibull distribution;
...
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1
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2k
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Is there a bivariate $\beta$ distribution I can fit to my data?
I am analyzing two dimensional data. After analyzing each dimension with the help of the fitdistrplus and logspline packages, they both fit the Beta distribution. Is it possible to analyze the two ...
- 71
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145
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Sum of Correlated Empirical pdf via Gaussian Copula
I'm new to R.
My goal is to calculate and plot the probability density function of the sum of 3 correlated empirical random variables (X1+X2+X3), given the correlation matrix.
I want to aggregate the ...
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Copula density bounds
I was wondering if someone can help me with a problem I encountered in my work. I need a bivariate copula density that meets two constraints at the bounds, and I have difficulties in finding one that ...
- 113
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1
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What does a copula density explain about dependence of random variables?
I am studying copulas and I find it difficult to understand what a copula density tells me about the dependence of random variables.
For example, if I have a Gaussian copula density, what can I say ...
- 71
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1
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518
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Copula density function
In the equation $h_t(x,y|...) = ...$, can anyone explain me why the first derivatives of the marginal distributions are included? $H_t$ is a distribution function and $h_t$ its density function.
...
- 51
4
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258
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Geometric construction of copula - question regarding C-volume
I am learning about copula's, using Nelsen's book, and more specifically about the geometric method of constructing copula's. The problem is replicated in the following link: http://www.stat.ubc.ca/...
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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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