Parametric statistics

About: Parametric statistics is a research topic. Over the lifetime, 39200 publications have been published within this topic receiving 765761 citations.

Modal interactions in the non-linear response of elastic cables under parametric/external excitation

Abstract: A theoretical model is derived which describes the non-linear response of a suspended elastic cable to small tangential oscillations of one support. The support oscillations, in general, result in parametric excitation of out-of-plane motion and simultaneous parametric and external excitation of in-plane motion. Cubic non-linearities due to cable stretching and quadratic nonlinearities due to equilibrium cable curvature couple these motion components in producing full, three-dimensional cable response. In this study, a two-degree-of-freedom approximation of the model is employed to examine a class of in-plane/out-of-plane motions that are coupled through the quadratic non-linearities. A first-order perturbation analysis is utilized to determine the existence and stability of the planar and non-planar periodic motions that result from simultaneous parametric and external resonances. The analysis leads to a bifurcation condition governing planar stability and results highlight how planar stability is reduced and non-planar response is enhanced whenever a “two-to-one” internal resonance condition exists between a pair of in-plane and out-of-plane cable modes. This two-to-one resonant behavior is clearly observed in experimental measurements of cable response which are also in good qualitative agreement with theoretical predictions.

Applications of parametric searching in geometric optimization

Abstract: We present several applications in computational geometry of Megiddo's parametric searching technique. These applications include; (1) Finding the minimum Hausdorff distance in the Euclidean metric between two polygonal regions under translation; (2) Computing the biggest line segment that can be placed inside a simple polygon; (3) Computing the smallest width annulus that can contain a given set of points in the plane; (4) Solving the 1-segment center problem—given a set of points in the plane, find a placement for a given line segment (under translation and rotation) which minimizes the largest distance from the segment to the given points; (5) Given a set of n points in 3-space, finding the largest radius r such that if we place a ball of radius r around each point, no segment connecting a pair of points is intersected by a third ball. Besides obtaining efficient solutions to all these problems (which, in every case, either improve considerably previous solutions or are the first non-trivial solutions to these problems), our goal is to demonstrate the versatility of the parametric searching technique.

Improving the simulation of extreme precipitation events by stochastic weather generators

Abstract: [1] Stochastic weather generators are commonly used to generate scenarios of climate variability or change on a daily timescale. So the realistic modeling of extreme events is essential. Presently, parametric weather generators do not produce a heavy enough upper tail for the distribution of daily precipitation amount, whereas those based on resampling have inherent limitations in representing extremes. Regarding this issue, we first describe advanced statistical tools from ultimate and penultimate extreme value theory to analyze and model extremal behavior of precipitation intensity (i.e., nonzero amount), which, although interesting in their own right, are mainly used to motivate approaches to improve the treatment of extremes within a weather generator framework. To this end we propose and discuss several possible approaches, none of which resolves the problem at hand completely, but at least one of them (i.e., a hybrid technique with a gamma distribution for low to moderate intensities and a generalized Pareto distribution for high intensities) can lead to a substantial improvement. An alternative approach, based on fitting the stretched exponential (or Weibull) distribution to either all or only high intensities, is found difficult to implement in practice.

Noiseless non-reciprocity in a parametric active device

Abstract: The use of microwaves to read and write information in superconducting qubits usually requires magnetic components that are difficult to integrate with chip-based circuits. A cascade of parametric amplifiers is now proposed instead, which could provide a more versatile and noise-free alternative.