Robust modeling using the generalized epsilon-skew-t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.

On the zeros of polynomials: an extension of the Enestrom-Kakeya theorem

This paper presents an extension of the Enestrom-Kakeya theorem concerning the roots of a polynomial that arises from the analysis of the stability of Brown (K, L) methods. The generalization relates to relaxing one of the inequalities on the coefficients of the polynomial. Two results concerning the zeros of polynomials will be proved, one of them providing a partial answer to a conjecture by Meneguette (1994)[6]. (C) 2011 Elsevier Inc. All rights reserved.

Interacting model for the cosmological dark sector

We discuss a new interacting model for the cosmological dark sector in which the attenuated dilution of cold dark matter scales as a(-3)f(a), where f(a) is an arbitrary function of the cosmic scale factor a. From thermodynamic arguments, we show that f(a) is proportional to the entropy source of the particle creation process. In order to investigate the cosmological consequences of this kind of interacting models, we expand f(a) in a power series, and viable cosmological solutions are obtained. Finally, we use current observational data to place constraints on the interacting function f(a).

Residence Time Distribution Models Derived from Non-Ideal Laminar Velocity Profiles in Tubes

The theoretical E-curve for the laminar flow of non-Newtonian fluids in circular tubes may not be accurate for real tubular systems with diffusion, mechanical vibration, wall roughness, pipe fittings, curves, coils, or corrugated walls. Deviations from the idealized laminar flow reactor (LFR) cannot be well represented using the axial dispersion or the tanks-in-series models of residence time distribution (RTD). In this work, four RTD models derived from non-ideal velocity profiles in segregated tube flow are proposed. They were used to represent the RTD of three tubular systems working with Newtonian and pseudoplastic fluids. Other RTD models were considered for comparison. The proposed models provided good adjustments, and it was possible to determine the active volumes. It is expected that these models can be useful for the analysis of LFR or for the evaluation of continuous thermal processing of viscous foods.

Comparing non-stationary and irregularly spaced time series

In this paper, we present approximate distributions for the ratio of the cumulative wavelet periodograms considering stationary and non-stationary time series generated from independent Gaussian processes. We also adapt an existing procedure to use this statistic and its approximate distribution in order to test if two regularly or irregularly spaced time series are realizations of the same generating process. Simulation studies show good size and power properties for the test statistic. An application with financial microdata illustrates the test usefulness. We conclude advocating the use of these approximate distributions instead of the ones obtained through randomizations, mainly in the case of irregular time series. (C) 2012 Elsevier B.V. All rights reserved.