Browsing by Subject "Dependence structures"

Now showing 1 - 2 of 2

Open Access
Joint mixability of some integer matrices
(Elsevier B.V., 2016) Bellini, F.; Karaşan, O. E.; Pınar, M. Ç.
We study the problem of permuting each column of a given matrix to achieve minimum maximal row sum or maximum minimal row sum, a problem of interest in probability theory and quantitative finance where quantiles of a random variable expressed as the sum of several random variables with unknown dependence structure are estimated. If the minimum maximal row sum is equal to the maximum minimal row sum the matrix has been termed jointly mixable (see e.g. Haus (2015), Wang and Wang (2015), Wang et al. (2013)). We show that the lack of joint mixability (the joint mixability gap) is not significant, i.e., the gap between the minimum maximal row sum and the maximum minimal row sum is either zero or one for a class of integer matrices including binary and complete consecutive integers matrices. For integer matrices where all entries are drawn from a given set of discrete values, we show that the gap can be as large as the difference between the maximal and minimal elements of the discrete set. The aforementioned result also leads to a polynomial-time approximation algorithm for matrices with restricted domain. Computing the gap for a {0,1,2}-matrix is proved to be equivalent to finding column permutations minimizing the difference between the maximum and minimum row sums. A polynomial procedure for computing the optimum difference by solving the maximum flow problem on an appropriate graph is given. © 2016 Elsevier B.V. All rights reserved.
Open Access
Quantifying input uncertainty in an assemble-to-order system simulation with correlated input variables of mixed types
(IEEE, 2014) Akçay, Alp; Biller, B.
We consider an assemble-to-order production system where the product demands and the time since the last customer arrival are not independent. The simulation of this system requires a multivariate input model that generates random input vectors with correlated discrete and continuous components. In this paper, we capture the dependence between input variables in an undirected graphical model and decouple the statistical estimation of the univariate input distributions and the underlying dependence measure into separate problems. The estimation errors due to finiteness of the real-world data introduce the so-called input uncertainty in the simulation output. We propose a method that accounts for input uncertainty by sampling the univariate empirical distribution functions via bootstrapping and by maintaining a posterior distribution of the precision matrix that corresponds to the dependence structure of the graphical model. The method improves the coverages of the confidence intervals for the expected profit the per period.