ASTIKhat {stpp}

Anisotropic Space-Time Inhomogeneous K-function

Description

Compute an estimation of the Anisotropic Space-Time inhomogeneous K-function.

Usage

ASTIKhat(xyt, s.region, t.region, lambda, dist, times, 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 bounding box of xyt[,1:2] 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.

dist

Vector of distances u at which \widehat{K}_{\phi}(r,t) is computed. If missing, the maximum of dist is given by \min(S_x,S_y)/4, where S_x and S_y represent the maximum width and height of the bounding box of s.region.

times

Vector of times v at which \widehat{K}_{\phi}(r,t) is computed. If missing, the maximum of times is given by (T_{\max} - T_{\min})/4, where T_{\min} and T_{\max} are the minimum and maximum of the time interval T.

lambda

Vector of values of the space-time intensity function evaluated at the points (x,y,t) in S\times T. If lambda is missing, the estimate of the anisotropic space-time K-function is computed as for the homogeneous case, i.e. considering n/|S\times T| as an estimate of the space-time intensity.

ang

Angle in radians at which \widehat{K}_{\phi}(r,t) is computed. The argument ang=2*pi by default.

correction

A character vector specifying the edge correction(s) to be applied among "border", "modified.border", "translate" and "none" (see STIKhat). The default is "border".

Value

A list containing:

AKhat

ndist x ntimes matrix containing values of \widehat{K}_{\phi}(u,t).

dist, times

Parameters passed in argument.

correction

The name(s) of the edge correction method(s) passed in argument.

Author(s)

Francisco J. Rodriguez-Cortes <[e-mail]>

References

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.