ETAS (version 0.4.9)

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

Description

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

Usage

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.

Value

A numeric value.

Details

For a given \(t\), \(x\) and \(y\), this function computes $$ \sum_{t_i < t} k(m_i)g(t - t_i)f(x - x_i, y - y_i|m_i).$$

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. 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. 10.1007/0-387-31144-0_15.

See Also

etas catalog

Examples

# NOT RUN {
  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)
# }
# NOT RUN {
# }