6533b7cefe1ef96bd1257190

RESEARCH PRODUCT

Kernel estimation and display of a five-dimensional conditional intensity function

Giada Adelfio

subject

Kernel density estimationlcsh:QC801-809Process (computing)Neighbourhood (graph theory)Kernel intensity estimator seismic activity multi-demensional point processExpected valuelcsh:QC1-999lcsh:Geophysics. Cosmic physicsStatisticsOrder (group theory)Effective methodPoint (geometry)lcsh:QSettore SECS-S/01 - Statisticalcsh:Sciencelcsh:PhysicsEvent (probability theory)Mathematics

description

The aim of this paper is to find a convenient and effective method of displaying some second order properties in a neighbourhood of a selected point of the process. The used techniques are based on very general high-dimensional nonparametric smoothing developed to define a more gen- eral version of the conditional intensity function introduced in earlier earthquake studies by Vere-Jones (1978). 1976) is commonly used for such a purpose in discussing the cumulative behavior of interpoint distances about an initial point. It is defined as the expected number of events falling within a given distance of the initial event, divided by the overall density (rate in 2-dimensions) of the process, say . Since it is defined as an average over many initial points, the K-function cannot be used to distinguish processes with the same (average) second order properties. As an alternative, Getis and Franklin (1987) suggested examining the behavior of the occurrence patterns in the neighbourhood of selected initial points developing a second order neighbor analysis of mapped point patterns. However, this method is not use-

10.5194/npg-17-237-2010https://www.nonlin-processes-geophys.net/17/237/2010/