2,612 research outputs found
Construction of asymmetric copulas and its application in two-dimensional reliability modelling
Copulas offer a useful tool in modelling the dependence among random variables. In the literature, most of the existing copulas are symmetric while data collected from the real world may exhibit asymmetric nature. This necessitates developing asymmetric copulas that can model such data. In the meantime, existing methods of modelling two-dimensional reliability data are not able to capture the tail dependence that exists between the pair of age and usage, which are the two dimensions designated to describe product life. This paper proposes two new methods of constructing asymmetric copulas, discusses the properties of the new copulas, and applies the method to fit two-dimensional reliability data that are collected from the real world
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
Characterizations of bivariate conic, extreme value, and Archimax copulas
Based on a general construction method by means of bivariate ultramodular copulas we construct, for particular settings, special bivariate conic, extreme value, and Archimax copulas. We also show that the sets of copulas obtained in this way are dense in the sets of all conic, extreme value, and Archimax copulas, respectively
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
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
copulaedas: An R Package for Estimation of Distribution Algorithms Based on Copulas
The use of copula-based models in EDAs (estimation of distribution
algorithms) is currently an active area of research. In this context, the
copulaedas package for R provides a platform where EDAs based on copulas can be
implemented and studied. The package offers complete implementations of various
EDAs based on copulas and vines, a group of well-known optimization problems,
and utility functions to study the performance of the algorithms. Newly
developed EDAs can be easily integrated into the package by extending an S4
class with generic functions for their main components. This paper presents
copulaedas by providing an overview of EDAs based on copulas, a description of
the implementation of the package, and an illustration of its use through
examples. The examples include running the EDAs defined in the package,
implementing new algorithms, and performing an empirical study to compare the
behavior of different algorithms on benchmark functions and a real-world
problem
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