scholarly journals Real-coded Crossovers as a Role of Kernel Density Estimator

2007 ◽  
Vol 22 ◽  
pp. 520-530
Author(s):  
Jun Sakuma ◽  
Shigenobu Kobayashi
Keyword(s):  
Kernel Density ◽  
Kernel Density Estimator ◽  
Density Estimator

scholarly journals Smooth Kernel Estimation of a Circular Density Function: A Connection to Orthogonal Polynomials on the Unit Circle

2018 ◽  
Vol 2018 ◽  
pp. 1-4 ◽  
Author(s):  
Yogendra P. Chaubey
Keyword(s):  
Orthogonal Polynomials ◽  
Unit Circle ◽  
Kernel Estimation ◽  
Kernel Density ◽  
Cauchy Distribution ◽  
Kernel Density Estimator ◽  
Circular Statistics ◽  
Cauchy Kernel ◽  
Density Estimator

The circular kernel density estimator, with the wrapped Cauchy kernel, is derived from the empirical version of Carathéodory function that is used in the literature on orthogonal polynomials on the unit circle. An equivalence between the resulting circular kernel density estimator, to Fourier series density estimator, has also been established. This adds further weight to the considerable role of the wrapped Cauchy distribution in circular statistics.

Effect of Epicenter Data Inconsistency in Determining Bandwidth and its Subsequent Use in Hazard Analysis for Chennai Using Kernel Smoothing Approach

2014 ◽  
Vol 5 (1) ◽  
pp. 21-38
Author(s):  
C. K. Ramanna ◽  
G. R. Dodagoudar
Keyword(s):  
Power Law ◽  
Tamil Nadu ◽  
Kernel Density ◽  
Kernel Density Estimator ◽  
Density Estimator ◽  
Earthquake Catalog ◽  
Return Periods ◽  
Spatial Activity ◽  
Activity Rate ◽  
Data Inconsistency

The most important parameter in the kernel density estimator is the bandwidth or spread or window width. The bandwidth of the kernel density estimator, which follows the power law, is determined using the nearest neighborhood technique for the earthquake catalog which is divided into bins. For reliable hazard estimates, the magnitude bins used in developing the power law and estimating the spatial activity rate density function should be the same. It is important that consistency be maintained between the earthquake epicenters used in determining the bandwidth and the epicenters to which the bandwidth is applied subsequently. In this paper, the effect of epicenter data inconsistency on hazard estimates for various return periods for Chennai is evaluated. Two methods of binning are used, one in which the epicenters used in deriving the bandwidth is in line with the epicenters used in arriving at the spatial activity rate and the other where the epicenters used in deriving the bandwidth are just grouped by dividing the catalogue into equal bins. Seismic hazard estimations are compared using these two approaches of forming the magnitude bins for Chennai, Tamil Nadu, India. The peak ground acceleration (PGA) values obtained from Binning Methods 1 and 2 for 475 years return period are 0.0955g and 0.0802g respectively. The difference in PGA and peak spectral acceleration (PSA) from the two binning methods ranges from 20 to 10% with respect to Binning Method 1 for the return periods of 72 to 2475 years.

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