1,528 research outputs found
Probabilistic modeling of flood characterizations with parametric and minimum information pair-copula model
This paper highlights the usefulness of the minimum information and parametric pair-copula construction (PCC) to model the joint distribution of flood event properties. Both of these models outperform other standard multivariate copula in modeling multivariate flood data that exhibiting complex patterns of dependence, particularly in the tails. In particular, the minimum information pair-copula model shows greater flexibility and produces better approximation of the joint probability density and corresponding measures have capability for effective hazard assessments. The study demonstrates that any multivariate density can be approximated to any degree of desired precision using minimum information pair-copula model and can be practically used for probabilistic flood hazard assessment
Copulas in finance and insurance
Copulas provide a potential useful modeling tool to represent the dependence structure
among variables and to generate joint distributions by combining given marginal
distributions. Simulations play a relevant role in finance and insurance. They are used to
replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so
on. Using copulas, it is easy to construct and simulate from multivariate distributions based
on almost any choice of marginals and any type of dependence structure. In this paper we
outline recent contributions of statistical modeling using copulas in finance and insurance.
We review issues related to the notion of copulas, copula families, copula-based dynamic and
static dependence structure, copulas and latent factor models and simulation of copulas.
Finally, we outline hot topics in copulas with a special focus on model selection and
goodness-of-fit testing
Learning Vine Copula Models For Synthetic Data Generation
A vine copula model is a flexible high-dimensional dependence model which
uses only bivariate building blocks. However, the number of possible
configurations of a vine copula grows exponentially as the number of variables
increases, making model selection a major challenge in development. In this
work, we formulate a vine structure learning problem with both vector and
reinforcement learning representation. We use neural network to find the
embeddings for the best possible vine model and generate a structure.
Throughout experiments on synthetic and real-world datasets, we show that our
proposed approach fits the data better in terms of log-likelihood. Moreover, we
demonstrate that the model is able to generate high-quality samples in a
variety of applications, making it a good candidate for synthetic data
generation
Nonparametric estimation of the tree structure of a nested Archimedean copula
One of the features inherent in nested Archimedean copulas, also called
hierarchical Archimedean copulas, is their rooted tree structure. A
nonparametric, rank-based method to estimate this structure is presented. The
idea is to represent the target structure as a set of trivariate structures,
each of which can be estimated individually with ease. Indeed, for any three
variables there are only four possible rooted tree structures and, based on a
sample, a choice can be made by performing comparisons between the three
bivariate margins of the empirical distribution of the three variables. The set
of estimated trivariate structures can then be used to build an estimate of the
target structure. The advantage of this estimation method is that it does not
require any parametric assumptions concerning the generator functions at the
nodes of the tree.Comment: 25 pages, 9 figure
Copulas in finance and insurance
Copulas provide a potential useful modeling tool to represent the dependence structure among variables and to generate joint distributions by combining given marginal distributions. Simulations play a relevant role in finance and insurance. They are used to replicate efficient frontiers or extremal values, to price options, to estimate joint risks, and so on. Using copulas, it is easy to construct and simulate from multivariate distributions based on almost any choice of marginals and any type of dependence structure. In this paper we outline recent contributions of statistical modeling using copulas in finance and insurance. We review issues related to the notion of copulas, copula families, copula-based dynamic and static dependence structure, copulas and latent factor models and simulation of copulas. Finally, we outline hot topics in copulas with a special focus on model selection and goodness-of-fit testing.Dependence structure, Extremal values, Copula modeling, Copula review
Constructing a bivariate distribution function with given marginals and correlation: application to the galaxy luminosity function
We show an analytic method to construct a bivariate distribution function
(DF) with given marginal distributions and correlation coefficient. We
introduce a convenient mathematical tool, called a copula, to connect two DFs
with any prescribed dependence structure. If the correlation of two variables
is weak (Pearson's correlation coefficient ), the
Farlie-Gumbel-Morgenstern (FGM) copula provides an intuitive and natural way
for constructing such a bivariate DF. When the linear correlation is stronger,
the FGM copula cannot work anymore. In this case, we propose to use a Gaussian
copula, which connects two given marginals and directly related to the linear
correlation coefficient between two variables. Using the copulas, we
constructed the BLFs and discuss its statistical properties. Especially, we
focused on the FUV--FIR BLF, since these two luminosities are related to the
star formation (SF) activity. Though both the FUV and FIR are related to the SF
activity, the univariate LFs have a very different functional form: former is
well described by the Schechter function whilst the latter has a much more
extended power-law like luminous end. We constructed the FUV-FIR BLFs by the
FGM and Gaussian copulas with different strength of correlation, and examined
their statistical properties. Then, we discuss some further possible
applications of the BLF: the problem of a multiband flux-limited sample
selection, the construction of the SF rate (SFR) function, and the construction
of the stellar mass of galaxies ()--specific SFR () relation. The
copulas turned out to be a very useful tool to investigate all these issues,
especially for including the complicated selection effects.Comment: 14 pages, 5 figures, accepted for publication in MNRAS
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