Uncertain Regression Modeling Given the Observational Distributions

In regression theory, the distribution of the error terms occupies a critical position, particularly when switching the data environment from probability theory to uncertainty theory. On the probabilistic platform, the variance-covariance matrix for standard regression model is assumed by an identity matrix with a positive constant multiplier. On the uncertain measure foundation, for given observational distributions, the variance-covariance is an interval-valued matrix. In this paper, we derive the interval-valued variance for given uncertain normal distribution. Further, we derive the interval-valued auto variance matrix for the observational error terms being the members of an uncertain canonical process. This new model may be regarded as an extension to the uncertain canonical process regression models, but its interval-valued variance-covariance matrix is also intrinsic to the uncertain canonical process, which results in an interval-valued weighted regression model

6 Sigma Rules under Uncertain Normal Distributions

In evaluating modeling quality, risk level and general quality management 6 sigma rules are popular among statisticians and quality engineers today. The 6 sigma rules of Gaussian distribution are very simple and elemental. If switching the working environment from the probability measure based to the uncertain measure based, the simple 6 sigma rules will be no longer simple. In this paper, we investigate the problems when facing Liu\u27s uncertain normal distribution which can only facilitate interval variance or standard deviation. Consequently, the way to define uncertain 6 sigma rules are described and discussed and thus those to practical applications

Bayesian component reliability assessment with system data

This work provides a Bayes approach to inference on a particular parameter p[subscript] 1, when the sample likelihood depends on p[subscript] 1 only through a function [theta] = g(p[subscript]1,p[subscript]2) of p[subscript] 1 and a second parameter p[subscript] 2; in this case, the posterior mean of p[subscript] 1 turns out to be a generalized posterior moment of [theta]. An example of this is the case when only system performance data are available, but component performance evaluation is desired;Bayes inference on p[subscript] 1 is addressed from both the small-sample and asymptotic point of view, including the comparison of the posterior mean of p[subscript] 1 with several of its approximations. For a certain special case of the system example above, hypergeometric forms are given for the posterior mean of p[subscript] 1, and its approximations.</p

Optimal Bespoke CDO Design via NSGA-II

This research work investigates the theoretical foundations and computational aspects of constructing optimal bespoke CDO structures. Due to the evolutionary nature of the CDO design process, stochastic search methods that mimic the metaphor of natural biological evolution are applied. For efficient searching the optimal solution, the nondominating sort genetic algorithm (NSGA-II) is used, which places emphasis on moving towards the true Paretooptimal region. This is an essential part of real-world credit structuring problems. The algorithm further demonstrates attractive constraint handling features among others, which is suitable for successfully solving the constrained portfolio optimisation problem. Numerical analysis is conducted on a bespoke CDO collateral portfolio constructed from constituents of the iTraxx Europe IG S5 CDS index. For comparative purposes, the default dependence structure is modelled via Gaussian and Clayton copula assumptions. This research concludes that CDO tranche returns at all levels of risk under the Clayton copula assumption performed better than the sub-optimal Gaussian assumption. It is evident that our research has provided meaningful guidance to CDO traders, for seeking significant improvement of returns over standardised CDOs tranches of similar rating