Kernel Estimation of Cumulative Residual Tsallis Entropy and Its Dynamic Version under ρ-Mixing Dependent Data

Tsallis introduced a non-logarithmic generalization of Shannon entropy, namely Tsallis entropy, which is non-extensive. Sati and Gupta proposed cumulative residual information based on this non-extensive entropy measure, namely cumulative residual Tsallis entropy (CRTE), and its dynamic version, namely dynamic cumulative residual Tsallis entropy (DCRTE). In the present paper, we propose non-parametric kernel type estimators for CRTE and DCRTE where the considered observations exhibit an ρ-mixing dependence condition. Asymptotic properties of the estimators were established under suitable regularity conditions. A numerical evaluation of the proposed estimator is exhibited and a Monte Carlo simulation study was carried out.

A Consistent Geological-Seismological Model For Earthquake Occurrence in New Zealand

<p>For the development of earthquake occurrence models, historical earthquake catalogues and compilations of mapped, active faults are often used. The goal of this study is to develop new methodologies for the generation of an earthquake occurrence model for New Zealand that is consistent with both data sets. For the construction of a seismological earthquake occurrence model based on the historical earthquake record, 'adaptive kernel estimation' has been used in this study. Based on this method a technique has been introduced to filter temporal sequences (e.g. aftershocks). Finally, a test has been developed for comparing different earthquake occurrence models. It has been found that the adaptive kernel estimation with temporal sequence filtering gives the best joint fit between the earthquake catalogue and the earthquake occurrence model, and between two earthquake occurrence models obtained from data from two independent time intervals. For the development of a geological earthquake occurrence model based on fault information, earthquake source relationships (i.e. rupture length versus rupture width scaling) have been revised. It has been found that large dip-slip and strike-slip earthquakes scale differently. Using these source relationships a dynamic stochastic fault model has been introduced. Whereas earthquake hazard studies often do not allow individual fault segments to produce compound ruptures, this model allows the linking of fault segments by chance. The moment release of simulated fault ruptures has been compared with the theoretical deformation along the plate boundary. When comparing the seismological and the geological earthquake occurrence model, it has been found that a 'good' occurrence model for large dip-slip earthquakes is given by the seismological occurrence model using the Gutenberg-Richter magnitude frequency distribution. In contrast, regions dominated by long strike-slip faults produce large earthquakes but not many small earthquakes and the occurrence of earthquakes on such faults should be inferred from the dynamic fault model.</p>

A Consistent Geological-Seismological Model For Earthquake Occurrence in New Zealand

<p>For the development of earthquake occurrence models, historical earthquake catalogues and compilations of mapped, active faults are often used. The goal of this study is to develop new methodologies for the generation of an earthquake occurrence model for New Zealand that is consistent with both data sets. For the construction of a seismological earthquake occurrence model based on the historical earthquake record, 'adaptive kernel estimation' has been used in this study. Based on this method a technique has been introduced to filter temporal sequences (e.g. aftershocks). Finally, a test has been developed for comparing different earthquake occurrence models. It has been found that the adaptive kernel estimation with temporal sequence filtering gives the best joint fit between the earthquake catalogue and the earthquake occurrence model, and between two earthquake occurrence models obtained from data from two independent time intervals. For the development of a geological earthquake occurrence model based on fault information, earthquake source relationships (i.e. rupture length versus rupture width scaling) have been revised. It has been found that large dip-slip and strike-slip earthquakes scale differently. Using these source relationships a dynamic stochastic fault model has been introduced. Whereas earthquake hazard studies often do not allow individual fault segments to produce compound ruptures, this model allows the linking of fault segments by chance. The moment release of simulated fault ruptures has been compared with the theoretical deformation along the plate boundary. When comparing the seismological and the geological earthquake occurrence model, it has been found that a 'good' occurrence model for large dip-slip earthquakes is given by the seismological occurrence model using the Gutenberg-Richter magnitude frequency distribution. In contrast, regions dominated by long strike-slip faults produce large earthquakes but not many small earthquakes and the occurrence of earthquakes on such faults should be inferred from the dynamic fault model.</p>

Sensitivity study of ring-shaped electrostatic sensor based on nonparametric estimation

In this paper, aiming at the problem of the electrostatic sensor signal satisfying the gaussian distribution, the non-parametric kernel estimation method is introduced, and the electrode induction model of the electrostatic sensor is finally fitted by combining the goodness of fit and the simulation data samples. This model satisfies the gaussian distribution and the electrostatic signal satisfying the gaussian distribution is given in the theory. Maxwell simulation software was used to simulate the theoretical sensitivity of the electrostatic sensor and the axial and radial spatial sensitivity characteristics of different sensor parameters were obtained. Within a certain range, the relative permittivity of the insulating tube is also discussed. Finally, an insulating tube with a relative permittivity of 3 is selected as the material of the insulating tube. Finally, the experiment is carried out on the experimental equipment and the conclusions obtained in the article are confirmed.

Application of regression in algorithm of nonlinear stochastic adaptation of unstable multidimensional objects

The results of a study of applicability of kernel estimation in the synergetic control systems for the objects unstable in an open-loop state (without a stabilizing control) have been presented. The effectiveness of kernel estimates has been shown for four nonlinear objects with unstable limiting states. The estimate the effectiveness of embedding the kernel predictive estimate of the state variables of a nonlinear object, subjected to disturbances of an unknown nature, into the system of synergetic control is demonstrated.