BIAS-CORRECTED MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF THE WEIGHTED LINDLEY DISTRIBUTION

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data applications. Therefore, some bias-corrected techniques for the MLEs are desired in practice, especially when the sample size is small. Two commonly used popular techniques to reduce the bias of the MLEs, are ‘preventive’ and ‘corrective’ approaches. They both can reduce the bias of the MLEs to order O(n−2), whereas the ‘preventive’ approach does not have an explicit closed form expression. Consequently, we mainly focus on the ‘corrective’ approach in this report. To illustrate the importance of the bias-correction in practice, we apply the bias-corrected method to two popular lifetime distributions: the inverse Lindley distribution and the weighted Lindley distribution. Numerical studies based on the two distributions show that the considered bias-corrected technique is highly recommended over other commonly used estimators without bias-correction. Therefore, special attention should be paid when we estimate the unknown parameters of the probability distributions under the scenario in which the sample size is small or moderate

Efficient Algorithms for Node Disjoint Subgraph Homeomorphism Determination

Recently, great efforts have been dedicated to researches on the management of large scale graph based data such as WWW, social networks, biological networks. In the study of graph based data management, node disjoint subgraph homeomorphism relation between graphs is more suitable than (sub)graph isomorphism in many cases, especially in those cases that node skipping and node mismatching are allowed. However, no efficient node disjoint subgraph homeomorphism determination (ndSHD) algorithms have been available. In this paper, we propose two computationally efficient ndSHD algorithms based on state spaces searching with backtracking, which employ many heuristics to prune the search spaces. Experimental results on synthetic data sets show that the proposed algorithms are efficient, require relative little time in most of the testing cases, can scale to large or dense graphs, and can accommodate to more complex fuzzy matching cases.Comment: 15 pages, 11 figures, submitted to DASFAA 200

Acoustic Bragg Reflectors for Q-Enhancement of Unreleased MEMS Resonators

This work presents the design of acoustic Bragg reflectors (ABRs) for unreleased MEMS resonators through analysis and simulation. Two of the greatest challenges to the successful implementation of MEMS are those of packaging and integration with integrated circuits. Development of unreleased RF MEMS resonators at the transistor level of the CMOS stack will enable direct integration into front-end-of-line (FEOL) processing, making these devices an attractive choice for on-chip signal generation and signal processing. The use of ABRs in unreleased resonators reduces spurious modes while maintaining high quality factors. Analysis on unreleased resonators using ABRs covers design principles, effects of fabrication variation, and comparison to released devices. Additionally, ABR-based unreleased resonators are compared with unreleased resonators enhanced using phononic crystals, showing order of magnitude higher quality factor (Q) for the ABR-based devices.United States. Defense Advanced Research Projects Agency (DARPA Young Faculty Award)Semiconductor Research Corporation (Center for Materials, Structures and Devices (MSD)

Positive almost periodic solutions for a class of nonlinear Duffing equations with a deviating argument

In this paper, we study a class of nonlinear Duffing equations with a deviating argument and establish some sufficient conditions for the existence of positive almost periodic solutions of the equation. These conditions are new and complement to previously known results