Compute an estimation of the Anisotropic Space-Time inhomogeneous \(K\)-function.
ASTIKhat(xyt, s.region, t.region, lambda, dist, times, ang,
correction = "border")A list containing:
ndist x ntimes matrix containing values of \(\widehat{K}_{\phi}(u,t)\).
Parameters passed in argument.
The name(s) of the edge correction method(s) passed in argument.
Coordinates and times \((x,y,t)\) of the point pattern.
Two-column matrix specifying polygonal region containing all data locations. If s.region is missing, the bounding box of xyt[,1:2] is considered.
Vector containing the minimum and maximum values of the time interval. If t.region is missing, the range of xyt[,3] is considered.
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.
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 \(T\).
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.
Angle in radians at which \(\widehat{K}_{\phi}(r,t)\) is computed. The argument ang=2*pi by default.
A character vector specifying the edge correction(s) to be applied among "border", "modified.border", "translate" and "none" (see STIKhat). The default is "border".
Francisco J. Rodriguez-Cortes <frrodriguezc@unal.edu.co>
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.