Related papers: A Natural Copula
We study the problem of estimating a sequence of evolving probability distributions from historical data, where the underlying distribution changes over time in a nonstationary and nonparametric manner. To capture gradual changes, we…
When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…
We propose notions of calibration for probabilistic forecasts of general multivariate quantities. Probabilistic copula calibration is a natural analogue of probabilistic calibration in the univariate setting. It can be assessed empirically…
The copula representations for conditionally independent random variables and the distribution properties of order statistics of these random variables are studied.
Copula models have become one of the most widely used tools in the applied modelling of multivariate data. Similarly, Bayesian methods are increasingly used to obtain efficient likelihood-based inference. However, to date, there has been…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
One of the main goals in non-life insurance is to estimate the claims reserve distribution. A generalized time series model, that allows for modeling the conditional mean and variance of the claim amounts, is proposed for the claims…
When modeling the distribution of a multivariate continuous random vector using the so-called \emph{copula approach}, it is not uncommon to have ties in the coordinate samples of the available data because of rounding or lack of measurement…
The Gaussian copula is a powerful tool that has been widely used to model spatial and/or temporal correlated data with arbitrary marginal distributions. However, this kind of model can potentially be too restrictive since it expresses a…
A key tool to carry out inference on the unknown copula when modeling a continuous multivariate distribution is a nonparametric estimator known as the empirical copula. One popular way of approximating its sampling distribution consists of…
An extension of the empirical copula is considered by combining an estimator of a multivariate cumulative distribution function with estimators of the marginal cumulative distribution functions for marginal estimators that are not…
This paper presents a new copula to model dependencies between insurance entities, by considering how insurance entities are affected by both macro and micro factors. The model used to build the copula assumes that the insurance losses of…
We utilize copulas to constitute a unified framework for constructing and optimizing variational proposals in hierarchical Bayesian models. For models with continuous and non-Gaussian hidden variables, we propose a semiparametric and…
In this paper, we study the identifiability and the estimation of the parameters of a copula-based multivariate model when the margins are unknown and are arbitrary, meaning that they can be continuous, discrete, or mixtures of continuous…
Modeling of high order multivariate probability distribution is a difficult problem which occurs in many fields. Copula approach is a good choice for this purpose, but the curse of dimensionality still remains a problem. In this paper we…
Analysing dependent risks is an important task for insurance companies. A dependency is reflected in the fact that information about one random variable provides information about the likely distribution of values of another random…
Given a random sample from a continuous multivariate distribution, Stute's representation is obtained for empirical copula processes constructed from a broad class of smooth, possibly data-adaptive nonparametric copula estimators. The…
In this paper, we pay our attention to geometric parameters and their applications in economics and finance. We discuss the multiplicative models in which a geometric mean and a geometric standard deviation are more natural than arithmetic…
We propose the extension of Fr\'{e}chet-Hoeffding copula bounds for circular data. The copula is a powerful tool for describing the dependency of random variables. In two dimensions, the Fr\'{e}chet-Hoeffding upper (lower) bound indicates…
Sklar's theorem is an important tool that connects bidimensional distribution functions with their marginals by means of a copula. When there is imprecision about the marginals, we can model the available information by means of p-boxes,…