lambda: Clustering Part of Conditional Intensity Function of the ETAS...

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/lambda.R

Description

A function to compute the clustering part of the conditional intensity function of the ETAS model at specified time and location.

Usage

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  lambda(t, x, y, param, object)

Arguments

t

A numeric value. The time that the conditional intensity is to be computed at.

x

A numeric value. The x-coordinate of the location that the conditional intensity is to be computed at.

y

A numeric value. The y-coordinate of the location that the conditional intensity is to be computed at.

param

Vector of model parameters.

object

An object of class "catalog" containing an earthquake catalog dataset.

Details

For a given t, x and y, this function computes

sum[t[i] < t] k(m[i]) g(t - t[i]) f(x - x[i], y - y[i]|m[i]).

Value

A numeric value.

Author(s)

Abdollah Jalilian jalilian@razi.ac.ir

References

Zhuang J, Ogata Y, Vere-Jones D (2002). Stochastic Declustering of Space-Time Earthquake Occurrences. Journal of the American Statistical Association, 97(458), 369–380. doi: 10.1198/016214502760046925.

Zhuang J, Ogata Y, Vere-Jones D (2006). Diagnostic Analysis of Space-Time Branching Processes for Earthquakes. In Case Studies in Spatial Point Process Modeling, pp. 275–292. Springer Nature. doi: 10.1007/0-387-31144-0_15.

See Also

etas catalog

Examples

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  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)

  param <- c(0.46, 0.23, 0.022, 2.8, 1.12, 0.012, 2.4, 0.35)

  ## Not run: 
  lambda(15706, 40.12, 34.5, param, iran.cat)
## End(Not run)

ETAS documentation built on March 16, 2021, 1:07 a.m.