Compute an estimation of the Anisotropic Space-Time inhomogeneous \(K\)-function.
ASTIKhat(xyt, s.region, t.region, lambda, dist, times, ang,
correction = "border")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".
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.
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.