A note on the Cauchy-type mixture distributions

An interesting class of continuous distributions, called Cauchy-type mixture, with potential applications in modelling erratic phenomena is introduced by Soltani and Tafakori [A class of continuous kernels and Cauchy type heavy tail distributions. Statist Probab Lett. 2013;83:1018–1027]. In this work, we provide more insights into the Cauchy-type mixture distributions, involving certain characterizations, connections with the generalized Linnik distributions and the class of discrete distributions induced by stable laws. We also prove that the Laplace transform of Cauchy-type mixture distributions when normalized by constant terms become as a density functions in terms of distributional conjugate property.     

A Novel Eigenvector Technique for Large Scale Combinatorial Problems in VLSI Layout

Modern integrated circuit design involves laying out circuits which consist of millions of switching elements or transistors. Due to the sheer complexity, optimizing the connectivity between transistors is a very difficult problem. How a circuit is interconnected is the single most important factor in performance criteria such as signal delay, power dissipation, circuit size and cost. These factors dictate that interconnections—wires, be made as short as possible. The wire–minimization problem is formulated as a sequence of discrete optimization subproblems. These problems are known to be NP-hard, hence they can only be solved approximately using meta-heuristics or linear programming techniques. Nevertheless, these methods are computationally expensive and the quality of solution depends to a great extent on an appropriate choice of starting configuration. A matrix reordering technique for solving very hard discrete optimization problems in Very Large Scale Integrated (VLSI) design which overcomes some of these shortcomings is proposed. In particular, the computational cost is reasonable—of the order of n ^1.4 running time.     

A new lifetime model with different types of failure rate

A new class of lifetime distributions, which can exhibit with upside-down bathtub-shaped, bathtub-shaped, decreasing, and increasing failure rates, is introduced. The new distribution is constructed by compounding generalized Weibull and logarithmic distributions, leading to improvement on the lifetime distribution considered in Dimitrakopoulou et al. (2007 Dimitrakopoulou, T., K. Adamidis, and S. Loukas. 2007. A lifetime distribution with an upside-down bathtub-shaped hazard function. IEEE Transactions on Reliability 56:308–11.[Crossref], [Web of Science ®] , [Google Scholar]) by having no restriction on the shape parameter and extending the result studied by Tahmasbi and Rezaei (2008 Tahmasbi, R., and S. Rezaei. 2008. A two-parameter lifetime distribution with decreasing failure rate. Computational Statistics and Data Analysis 52:3889–901.[Crossref], [Web of Science ®] , [Google Scholar]) in the general form. The proposed model includes the exponential–logarithmic and Weibull–logarithmic distributions as special cases. Various statistical properties of the proposed class are discussed. Furthermore, estimation via the maximum likelihood method and the Fisher information matrix are discussed. Applications to real data demonstrate that the new class of distributions is more flexible than other recently proposed classes.