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

In ETAS: Modeling Earthquake Data Using 'ETAS' Model

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.

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 [e-mail]

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/0-387-31144-0_15")}.

See Also

etas catalog

Examples

  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 Sept. 30, 2024, 9:42 a.m.