scholarly journals Inducing a Target Association between Ordinal Variables by Using a Parametric Copula Family

2020 ◽  
Vol 49 (4) ◽  
pp. 9-18
Author(s):  
Alessandro Barbiero
Keyword(s):  
Linear Correlation ◽  
Random Variables ◽  
Marginal Distributions ◽  
Ordinal Variables ◽  
Fields Of Study ◽  
Copula Parameter ◽  
Distribution Matching ◽  
Target Association ◽  
Bivariate Copula ◽  
Parametric Copula

The need for building and generating statistically dependent random variables arises in various fields of study where simulation has proven to be a useful tool.In this work, we present an approach for constructing ordinal variables with arbitrarily assigned marginal distributions and value of association or correlation, expressed in terms of either Goodman and Kruskal's gamma or Pearson's linear correlation. The approach first constructs a class of bivariate copula-based distributions matching the assigned margins, and then, within this class, identifies the distribution matching the assigned association or correlation, by calibrating the copula parameter. A numerical example and a possible application are illustrated.

scholarly journals Inference for copula modeling of discrete data: a cautionary tale and some facts

2017 ◽  
Vol 5 (1) ◽  
pp. 121-132 ◽  
Author(s):  
Olivier P. Faugeras
Keyword(s):  
Model Misspecification ◽  
Discrete Data ◽  
Cautionary Tale ◽  
Copula Models ◽  
Problematic Use ◽  
Copula Modeling ◽  
Copula Parameter ◽  
Parametric Copula

AbstractIn this note, we elucidate some of the mathematical, statistical and epistemological issues involved in using copulas to model discrete data. We contrast the possible use of (nonparametric) copula methods versus the problematic use of parametric copula models. For the latter, we stress, among other issues, the possibility of obtaining impossible models, arising from model misspecification or unidentifiability of the copula parameter.

Probability theory and mathematical statistics

2021 ◽  
Author(s):  
Irina Paliy
Keyword(s):  
Probability Theory ◽  
Queuing Theory ◽  
Interval Estimation ◽  
Random Variables ◽  
Mathematical Statistics ◽  
Estimation Of Parameters ◽  
Introductory Course ◽  
Fields Of Study ◽  
Discrete Random Variables ◽  
Statistical Hypotheses

The tutorial is an introductory course in probability theory and mathematical statistics. Elements of combinatorics, basic concepts and theorems of probability theory, discrete random variables, continuous random variables, some limit theorems, one-dimensional and two-dimensional samples, point and interval estimation of parameters of the general population, testing of statistical hypotheses, elements of queuing theory are considered. The presentation of the theoretical material is accompanied by a large number of detailed examples of problem solving. For students of technical and economic fields of study and specialties, studying under the bachelor's and specialty programs.

Dependent Random Variables with Independent Subsets - II

1990 ◽  
Vol 33 (1) ◽  
pp. 24-28 ◽  
Author(s):  
Y. H. Wang
Keyword(s):  
Joint Distribution ◽  
Random Variables ◽  
Marginal Distributions ◽  
Dependent Random Variables ◽  
One Dimensional ◽  
The One

AbstractIn this paper, we consolidate into one two separate problems - dependent random variables with independent subsets and construction of a joint distribution with given marginals. Let N = {1,2,3,...} and X = {Xn; n ∊ N} be a sequence of random variables with nondegenerate one-dimensional marginal distributions {Fn; n ∊ N}. An example is constructed to show that there exists a sequence of random variables Y = {Yn; n ∊ N} such that the components of a subset of Y are independent if and only if its size is ≦ k, where k ≧ 2 is a prefixed integer. Furthermore, the one-dimensional marginal distributions of Y are those of X.

scholarly journals Estimating Differential Entropy using Recursive Copula Splitting

Entropy ◽  
2020 ◽  
Vol 22 (2) ◽  
pp. 236 ◽  
Author(s):  
Gil Ariel ◽  
Yoram Louzoun
Keyword(s):  
Compact Support ◽  
Mixed Type ◽  
Random Variables ◽  
Differential Entropy ◽  
High Dimensions ◽  
Marginal Distributions ◽  
Numerical Examples ◽  
One Dimensional ◽  
Different Dimensions

A method for estimating the Shannon differential entropy of multidimensional random variables using independent samples is described. The method is based on decomposing the distribution into a product of marginal distributions and joint dependency, also known as the copula. The entropy of marginals is estimated using one-dimensional methods. The entropy of the copula, which always has a compact support, is estimated recursively by splitting the data along statistically dependent dimensions. The method can be applied both for distributions with compact and non-compact supports, which is imperative when the support is not known or of a mixed type (in different dimensions). At high dimensions (larger than 20), numerical examples demonstrate that our method is not only more accurate, but also significantly more efficient than existing approaches.

scholarly journals Modelling the Dependency between Inflation and Exchange Rate Using Copula

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Charles Kwofie ◽  
Isaac Akoto ◽  
Kwaku Opoku-Ameyaw
Keyword(s):  
Exchange Rate ◽  
Random Variables ◽  
Garch Model ◽  
Unit Interval ◽  
Marginal Distributions ◽  
Copula Approach

In this paper, we propose a copula approach in measuring the dependency between inflation and exchange rate. In unveiling this dependency, we first estimated the best GARCH model for the two variables. Then, we derived the marginal distributions of the standardised residuals from the GARCH. The Laplace and generalised t distributions best modelled the residuals of the GARCH(1,1) models, respectively, for inflation and exchange rate. These marginals were then used to transform the standardised residuals into uniform random variables on a unit interval [0, 1] for estimating the copulas. Our results show that the dependency between inflation and exchange rate in Ghana is approximately 7%.

Sharp Bounds for Sums of Dependent Risks

2013 ◽  
Vol 50 (01) ◽  
pp. 42-53 ◽  
Author(s):  
Giovanni Puccetti ◽  
Ludger Rüschendorf
Keyword(s):  
Random Variables ◽  
Dependence Structure ◽  
Homogeneous Case ◽  
Marginal Distributions ◽  
Sharp Bounds ◽  
Duality Result ◽  
Dependent Risks ◽  
Monotone Densities ◽  
Monotone Density ◽  
Dual Bounds

Sharp tail bounds for the sum of d random variables with given marginal distributions and arbitrary dependence structure have been known since Makarov (1981) and Rüschendorf (1982) for d=2 and, in some examples, for d≥3. Based on a duality result, dual bounds have been introduced in Embrechts and Puccetti (2006b). In the homogeneous case, F 1=···=F n , with monotone density, sharp tail bounds were recently found in Wang and Wang (2011). In this paper we establish the sharpness of the dual bounds in the homogeneous case under general conditions which include, in particular, the case of monotone densities and concave densities. We derive the corresponding optimal couplings and also give an effective method to calculate the sharp bounds.

Reliability Based Design Optimization With Correlated Input Variables Using Copulas

2007 ◽  
Author(s):  
Kyung K. Choi ◽  
Yoojeong Noh ◽  
Liu Du
Keyword(s):  
Reliability Analysis ◽  
Random Variables ◽  
Performance Measure ◽  
Gaussian Copula ◽  
Joint Probability Distribution ◽  
Random Input ◽  
Marginal Distributions ◽  
Wide Range ◽  
Input Variables ◽  
Nataf Transformation

For the performance measure approach (PMA) of RBDO, a transformation between the input random variables and the standard normal random variables is necessary to carry out the inverse reliability analysis. For reliability analysis, Rosenblatt and Nataf transformations are commonly used. In many industrial RBDO problems, the input random variables are correlated. However, often only limited information such as the marginal distribution and covariance could be practically obtained, and the input joint probability distribution function (PDF) is very difficult to obtain. Thus, in literature, most RBDO methods assume all input random variables are independent. However, in this paper, it is found that the RBDO results can be significantly different when the input variables are correlated. Thus, various transformation methods are investigated for development of a RBDO method for problems with correlated input variables. It is found that Rosenblatt transformation is impractical for problems with correlated input variables due to difficulty of constructing a joint PDF from the marginal distributions and covariance. On the other hand, Nataf transformation can construct the joint CDF using the marginal distributions and covariance, and thus applicable to problems with correlated random input variables. The joint CDF is Nataf model, which is called a Gaussian copula in the copula family. Since the Gaussian copula can describe a wide range of the correlation coefficient, Nataf transformation can be widely used for various types of correlated input variables. In this paper, Nataf transformation is used to develop a RBDO method for design problems with correlated random input variables. Numerical examples are used to demonstrate the proposed method. Also, it is shown that the correlated random input variables significantly affect the RBDO results.

Sign in / Sign up

Export Citation Format

Share Document