Clustering Part of Conditional Intensity Function of the ETAS Model

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Description

A function to estimate the background seismicity rate and clustering (triggering) coefficient for a fitted ETAS model.

Usage

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  rates(fit, dimyx=NULL, method="zhuang", plot.it=TRUE)

Arguments

fit

A fitted ETAS model. An object of class "etas".

dimyx

Dimensions of the rectangular discretization grid for the goegraphical study region. A numeric vector of length 2.

method

A character string specifying the method of smoothing. Currently methods "zhuang" and "spatstat" are implemented.

plot.it

Logical flag indicating whether to plot the rates or return them as pixel images.

Details

The argument dimyx determines the rectangular discretization grid dimensions. If it is given, then it must be a numeric vector of length 2 where the forst component dimyx[1] is the number of subdivisions in the y-direction (latitude) and the second component dimyx[2] is the number of subdivisions in the x-direction (longitude). The default (NULL) sets it to be dimyx=c(128, 128).

Value

If plot.it=TRUE, the function produces plots of the background seismicity rate and clustering coefficient.

If plot.it=FALSE, it returns a list of length 3, with the total spatial intensity, background seismicity rate and clustering as components (objects of im class in the package spatstat).

Author(s)

Abdollah Jalilian jalilian@razi.ac.ir

References

Zhuang, J., Ogata, Y. and Vere-Jones, D. (2005). Diagnostic analysis of space-time branching processes for earthquakes. Lecture Note in Statistics: Case Studies in Spatial Point Process Models (Baddeley, A., Gregori, P., Mateu, J., Stoica, R. and Stoyan, D.), Springer-Verlag, New York, 185, 276–292.

Zhuang, J., Ogata, Y. and Vere-Jones, D. (2002). Stochastic declustering of space-time earthquake occurrences. Journal of the American Statistical Association, 97, 369–380.

See Also

etas

Examples

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  # preparing the catalog
  iran.cat <- catalog(iran.quakes, time.begin="1973/01/01",
     study.start="1996/01/01", study.end="2016/01/01",
     lat.range=c(25, 42), long.range=c(42, 63), mag.threshold=4.5)

  print(iran.cat)
  ## Not run: 
  plot(iran.cat)
## End(Not run)

  # initial parameters values
  param01 <- c(0.46, 0.23, 0.022, 2.8, 1.12, 0.012, 2.4, 0.35)

  # fitting the model and estimating the rates
  ## Not run: 
  iran.fit <- etas(iran.cat, param0=param01, no.itr=5)
  rates(iran.fit, dimyx=c(200, 250))
  iran.rates <- rates(iran.fit, dimyx=c(200, 250), plot.it=FALSE)
  summary(iran.rates$background)
## End(Not run)