236 research outputs found
Emulation of Poincaré return maps with Gaussian Kriging models
In this paper we investigate the use of Gaussian emulators to give an accurate and computationally fast method to approximate return maps, a tool used to study the dynamics of differential equations. One advantage of emulators over other approximation techniques is that they encode deterministic data exactly, so where values of the return map are known these are also outputs of the emulator output, another is that emulators allow us to simultaneously emulate a parameterized family of ODEs giving a tool to assess the behavior of perturbed systems. The methods introduced here are illustrated using two well-known dynamical systems: The Rossler equations, and the Billiard system. We show that the method can be used to look at return maps and discuss the further implications for full computation of differential equation outputs
Estimation of Stress-Strength model in the Generalized Linear Failure Rate Distribution
In this paper, we study the estimation of , also so-called the
stress-strength model, when both and are two independent random
variables with the generalized linear failure rate distributions, under
different assumptions about their parameters. We address the maximum likelihood
estimator (MLE) of and the associated asymptotic confidence interval. In
addition, we compute the MLE and the corresponding Bootstrap confidence
interval when the sample sizes are small. The Bayes estimates of and the
associated credible intervals are also investigated. An extensive computer
simulation is implemented to compare the performances of the proposed
estimators. Eventually, we briefly study the estimation of this model when the
data obtained from both distributions are progressively type-II censored. We
present the MLE and the corresponding confidence interval under three different
progressive censoring schemes. We also analysis a set of real data for
illustrative purpose.Comment: 31 pages, 2 figures, preprin
Approximating multivariate distributions with vines
In a series of papers, Bedford and Cooke used vine (or pair-copulae) as a graphical tool for representing complex high dimensional distributions in terms of bivariate and conditional bivariate distributions or copulae. In this paper, we show that how vines can be used to approximate any given multivariate distribution to any required degree of approximation. This paper is more about the approximation rather than optimal estimation methods. To maintain uniform approximation in the class of copulae used to build the corresponding vine we use minimum information approaches. We generalised the results found by Bedford and Cooke that if a minimal information copula satis¯es each of the (local) constraints (on moments, rank correlation, etc.), then the resulting joint distribution will be also minimally informative given those constraints, to all regular vines. We then apply our results to modelling a dataset of Norwegian financial data that was previously analysed in Aas et al. (2009)
Symmetry properties of subdivision graphs
The subdivision graph of a graph is obtained from
by `adding a vertex' in the middle of every edge of \Si. Various
symmetry properties of are studied. We prove that, for a connected
graph , is locally -arc transitive if and only if
is -arc transitive. The diameter of
is , where has diameter and , and local -distance transitivity of is
defined for . In the general case where
we prove that is locally -distance transitive
if and only if is -arc transitive. For the
remaining values of , namely , we classify
the graphs for which is locally -distance transitive in
the cases, and . The cases remain open
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