pgraph {SAPP}

Graphical Outputs for the Point Process Data Set

Description

Provide the several graphical outputs for the point process data set.

Usage

pgraph(data, mag, threshold = 0.0, h, npoint, days, delta = 0.0, dmax = 0.0,
       separate.graphics = FALSE)

Arguments

data

point process data.

mag

magnitude.

threshold

threshold magnitude.

h

time length of the moving interval in which points are counted to show the graph.

npoint

number of subintervals in (0, days) to estimate a nonparametric intensity under the palm probability measure.

days

length of interval to display the intensity estimate under the palm probability.

delta

length of a subinterval unit in (0, dmax) to compute the variance time curve.

dmax

time length of an interval to display the variance time curve;
this is less than (length of whole interval)/4. As the default setting of either delta = 0.0 or dmax = 0.0, set dmax = (length of whole interval)/4 and delta = dmax/100.

separate.graphics

logical. If TRUE a graphic device is opened for each graphics display.

Value

cnum

cumulative numbers of events time.

lintv

interval length.

tau

= time * (total number of events)/(time end).

nevent

number of events in [tau, tau+h].

survivor

log survivor curve with i*(standard error), i = 1,2,3.

deviation

deviation of survivor function from the Poisson.

nomal.cnum

normalized cumulative number.

nomal.lintv

U(i) = -exp(-(normalized interval length)).

success.intv

successive pair of intervals.

occur

occurrence rate.

time

time assuming the stationary Poisson process.

variance

Var(N(0,time)).

error

the 0.95 and 0.99 error lines assuming the stationary Poisson process.

References

Ogata, Y., Katsura, K. and Zhuang, J. (2006) Computer Science Monographs, No.32, TIMSAC84: STATISTICAL ANALYSIS OF SERIES OF EVENTS (TIMSAC84-SASE) VERSION 2. The Institute of Statistical Mathematics.

Ogata, Y. (2006) Computer Science Monographs, No.33, Statistical Analysis of Seismicity - updated version (SASeies2006). The Institute of Statistical Mathematics.

Ogata, Y. and Shimazaki, K. (1984) Transition from aftershock to normal activity: The 1965 Rat islands earthquake aftershock sequence. Bulletin of the seismological society of America, vol. 74, no. 5, pp. 1757-1765.

Examples

## The aftershock data of 26th July 2003 earthquake of M6.2
data(main2003JUL26)
x <- main2003JUL26
pgraph(x$time, x$magnitude, h = 6, npoint = 100, days = 10)

## The residual point process data of 26th July 2003 earthquake of M6.2
data(res2003JUL26)
y <- res2003JUL26
pgraph(y$trans.time, y$magnitude, h = 6, npoint = 100, days = 10)