Generalized beta generated distributions

This article introduces generalized beta-generated (GBG) distributions. Sub-models include all classical beta-generated, Kumaraswamy-generated and exponentiated distributions. They are maximum entropy distributions under three intuitive conditions, which show that the classical beta generator skewness parameters only control tail entropy and an additional shape parameter is needed to add entropy to the centre of the parent distribution. This parameter controls skewness without necessarily differentiating tail weights. The GBG class also has tractable properties: we present various expansions for moments, generating function and quantiles. The model parameters are estimated by maximum likelihood and the usefulness of the new class is illustrated by means of some real data sets.

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

Robust control system design for generalized state-space systems

Robustness in multi-variable control system design requires that the solution to the design problem be insensitive to perturbations in the system data. In this paper we discuss measures of robustness for generalized state-space, or descriptor, systems and describe algorithmic techniques for optimizing robustness for various applications.

Hypothesis management in situation assessment

A situation assessment uses reports from sensors to produce hypotheses about a situation at a level of aggregation that is of direct interest to a military commander. A low level of aggregation could mean forming tracks from reports, which is well documented in the tracking literature as track initiation and data association. In this paper there is also discussion on higher level aggregation; assessing the membership of tracks to larger groups. Ideas used in joint tracking and identification are extended, using multi-entity Bayesian networks to model a number of static variables, of which the identity of a target is one. For higher level aggregation a scheme for hypothesis management is required. It is shown how an offline clustering of vehicles can be reduced to an assignment problem.

Keeping the dream of rigorous hypothesis testing alive

This article reviews recent work on hypothesis testing in the American Journal of AGricultural Economics and its predecessor journal, the Journal of Farm Economics

'Quasi'-norm of an arithmetical convolution operator and the order of the Riemann zeta function

In this paper we study Dirichlet convolution with a given arithmetical function f as a linear mapping 'f that sends a sequence (an) to (bn) where bn = Pdjn f(d)an=d. We investigate when this is a bounded operator on l2 and ¯nd the operator norm. Of particular interest is the case f(n) = n¡® for its connection to the Riemann zeta function on the line 1, 'f is bounded with k'f k = ³(®). For the unbounded case, we show that 'f : M2 ! M2 where M2 is the subset of l2 of multiplicative sequences, for many f 2 M2. Consequently, we study the `quasi'-norm sup kak = T a 2M2 k'fak kak for large T, which measures the `size' of 'f on M2. For the f(n) = n¡® case, we show this quasi-norm has a striking resemblance to the conjectured maximal order of j³(® + iT )j for ® > 12 .

Symmetric stability of compressible zonal flows on a generalized equatorial β plane

Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial � plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

A generalized collectively compact operator theory with an application to integral equations on unbounded domains

In this paper a generalization of collectively compact operator theory in Banach spaces is developed. A feature of the new theory is that the operators involved are no longer required to be compact in the norm topology. Instead it is required that the image of a bounded set under the operator family is sequentially compact in a weaker topology. As an application, the theory developed is used to establish solvability results for a class of systems of second kind integral equations on unbounded domains, this class including in particular systems of Wiener-Hopf integral equations with L1 convolutions kernels

Why all counter-evidence to the critical period hypothesis in second language acquisition is not equal or problematic

That adult and child language acquisitions differ in route and outcome is observable. Notwithstanding, there is controversy as to what this observation means for the Critical Period Hypothesis’ (CPH) application to adult second language acquisition (SLA). As most versions of the CPH applied to SLA claim that differences result from maturational effects on in-born linguistic mechanisms, the CPH has many implications that are amendable to empirical investigation. To date, there is no shortage of literature claiming that the CPH applies or does not apply to normal adult SLA. Herein, I provide an epistemological discussion on the conceptual usefulness of the CPH in SLA (cf. Singleton 2005) coupled with a review of Long's (2005) evaluation of much available relevant research. Crucially, I review studies that Long did not consider and conclude differently that there is no critical/sensitive period for L2 syntactic and semantic acquisition.

Aspect selection in adult L2 Spanish and the competing systems hypothesis: when pedagogical and linguistic rules conflict.

Native-like use of preterit and imperfect morphology in all contexts by English learners of L2 Spanish is the exception rather than the rule, even for successful learners. Nevertheless, recent research has demonstrated that advanced English learners of L2 Spanish attain a native-like morphosyntactic competence for the preterit/imperfect contrast, as evidenced by their native-like knowledge of associated semantic entailments (Goodin-Mayeda and Rothman 2007, Montrul and Slabakova 2003, Slabakova and Montrul 2003, Rothman and Iverson 2007). In addition to an L2 disassociation of morphology and syntax (e.g., Bruhn de Garavito 2003, Lardiere 1998, 2000, 2005, Prévost and White 1999, 2000, Schwartz 2003), I hypothesize that a system of learned pedagogical rules contributes to target-deviant L2 performance in this domain through the most advanced stages of L2 acquisition via its competition with the generative system. I call this hypothesis the Competing Systems Hypothesis. To test its predictions, I compare and contrast the use of the preterit and imperfect in two production tasks by native, tutored (classroom), and naturalistic learners of L2 Spanish.