HASTKfunct: Inhomogeneous anisotropic spatio-temporal K-function

In frajaroco/SOAstpp: Second-order analysis for anisotropic spatio-temporal point process data

Description

This function compute an estimation of the inhomogeneous anisotropic spatio-temporal K-function

Usage

HASTKfunct(xyt, s.region, t.region, lambda, ds, dt, ang,
  correction = "border")

Arguments

xyt	Coordinates and times (x,y,t) of the point pattern.
s.region	Two-column matrix specifying polygonal region containing all data locations. If s.region is missing, the Ripley-Rasson estimate of the spatial domain is considered.
t.region	Vector containing the minimum and maximum values of the time interval. If t.region is missing, the range of xyt[,3] is considered.
lambda	Vector of values of the spatio-temporal intensity function evaluated at the points (x,y,t) in W x T. If lambda is missing, the estimate of the anisotropic spatio-temporal K-function is computed as for the homogeneous case, i.e. considering n/|W x T| as an estimate of the spatio-temporal intensity.
ds	Vector of distances u at which \hat{K}_{φ}(r,t) is computed.
dt	Vector of times v at which \hat{K}_{φ}(r,t) is computed.
ang	Vector of angles in radians at which \hat{K}_{φ}(r,t) is computed. If ang is missing, the function HASTKfunct is evaluated in the vector common angles.
correction	A character vector specifying the edge correction(s) to be applied among "border", "modified.border", "translate" and "none". The default is "border".

Value

A list containing:

• astkl: Array containing nds by ndt matrices whose elements are \hat{K}_{φ}(r,t) evaluated in each ang-vector.

• ds: If dist is missing, a vector of distances u at which \hat{K}_{φ}(u,v) is computed.

• dt: If times is missing, a vector of distances v at which \hat{K}_{φ}(u,v) is computed.

• lambda: Value of the estimation of \hat{ρ}^{2}.

• ang: If ang is missing, the function si evalueten on the vector (pi/6,pi/4,pi/3,pi/2,2pi/3,3pi/4,5pi/6,pi).

Author(s)

Francisco J. Rodriguez-Cortes <[e-mail]> https://fjrodriguezcortes.wordpress.com

References

Gabriel, E., Rowlingson, B., Diggle P J. (2013). stpp: an R package for plotting, simulating and analyzing Spatio-Temporal Point Patterns. Journal of Statistical Software 53, 1-29.

Illian, J. B., Penttinen, A., Stoyan, H. and Stoyan, D. (2008). Statistical Analysis and Modelling of Spatial Point Patterns. John Wiley and Sons, London.

Gonzalez, J. A., Rodriguez-Cortes, F. J., Cronie, O., Mateu, J. (2016). Spatio-temporal point process statistics: a review. Spatial Statistics. Accepted.

Ohser, J. and D. Stoyan (1981). On the second-order and orientation analysis of planar stationary point processes. Biometrical Journal 23, 523-533.

Examples

## Not run:
#################

# Realisations of the homogeneous spatio-temporal Poisson processes
stp <- rpp(100)$xyt
# Generated spatio-temporal point pattern
plot(stp)

# Estimation of the anisotropic homogeneous spatio-temporal K-functions
out <- HASTKfunct(stp)

z1 <- out$astkf[,,1]
z2 <- out$astkf[,,2]
z3 <- out$astkf[,,3]
z4 <- out$astkf[,,4]

# Plot
par(mfrow=c(2,2))
persp(out$ds,out$dt,z1,theta=-45,phi=30,zlim=range(z1,na.rm=TRUE),ticktype="detailed",xlab="\n r = distance",ylab="\n t = time",zlab="",nticks=6,cex.axis=1.3,cex.lab=1.7)
persp(out$ds,out$dt,z2,theta=-45,phi=30,zlim=range(z2,na.rm=TRUE),ticktype="detailed",xlab="\n r = distance",ylab="\n t = time",zlab="",nticks=6,cex.axis=1.3,cex.lab=1.7)
persp(out$ds,out$dt,z3,theta=-45,phi=30,zlim=range(z3,na.rm=TRUE),ticktype="detailed",xlab="\n r = distance",ylab="\n t = time",zlab="",nticks=6,cex.axis=1.3,cex.lab=1.7)
persp(out$ds,out$dt,z4,theta=-45,phi=30,zlim=range(z4,na.rm=TRUE),ticktype="detailed",xlab="\n r = distance",ylab="\n t = time",zlab="",nticks=6,cex.axis=1.3,cex.lab=1.7)

## End(Not run)
#################

frajaroco/SOAstpp documentation built on Nov. 8, 2019, 2:17 a.m.