khat                 package:splancs                 R Documentation

_K-_f_u_n_c_t_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     Calculates an estimate of the K-function

_U_s_a_g_e:

     khat(pts,poly,s,newstyle=FALSE,checkpoly=TRUE)
     ## S3 method for class 'khat':
     print(x, ...)
     ## S3 method for class 'khat':
     plot(x, ...)

_A_r_g_u_m_e_n_t_s:

     pts: A points data set 

    poly: A polygon containing the points - must be a perimeter ring of
          points 

       s: A vector of distances at which to calculate the K function 

newstyle: if TRUE, the function returns a khat object

checkpoly: if TRUE compare polygon area and polygon bounding box and
          convex hull areas to see whether the polygon object is
          malformed; may be set to FALSE if the polygon is known to be
          a ring of points

       x: a 'khat' object

     ...: other arguments passed to plot and print functions

_D_e_t_a_i_l_s:

     The K function is defined as the expected number of further points
     within a distance s of an arbitrary point, divided by the overall
     density of the points.  In practice an edge-correction is required
     to avoid biasing the estimation due to non-recording of points
     outside the polygon.

     The newstyle argument and khat object were introduced in
     collaboration  with Thomas de Cornulier to permit the mapping of 
     counts or khats for chosen distance values, as in  <URL:
     ftp://pbil.univ-lyon1.fr/pub/mac/ADE/ADE4/DocThemPDFUS/Thema81.pdf
     >, p.18.

_V_a_l_u_e:

     If 'newstyle' is FALSE,  a vector like 's' containing the value of
     K at the points in 's'. else a 'khat' object list with: 

    khat: the value of K at the points in 's'

  counts: integer matrix of counts of points within the vector of
          distances 's' for each point

   khats: matrix of values of K within the vector of distances 's' for
          each point

       s: 's'

_R_e_f_e_r_e_n_c_e_s:

     Ripley, B.D. 1976 The second-order analysis of stationary point
     processes, _ J. Appl. Prob, 13_ 255-266; Rowlingson, B. and
     Diggle, P. 1993 Splancs: spatial point pattern analysis code in
     S-Plus.  Computers and Geosciences, 19, 627-655; the original
     sources can be accessed at: <URL:
     http://www.maths.lancs.ac.uk/~rowlings/Splancs/>. See also Bivand,
     R. and Gebhardt, A. 2000 Implementing functions for spatial
     statistical analysis using the R language. Journal of Geographical
     Systems, 2, 307-317.

_S_e_e _A_l_s_o:

     'Kenv.csr'

_E_x_a_m_p_l_e_s:

     data(cardiff)
     s <- seq(2,30,2)
     plot(s, sqrt(khat(as.points(cardiff), cardiff$poly, s)/pi) - s,
      type="l", xlab="Splancs - polygon boundary", ylab="Estimated L",
      ylim=c(-1,1.5))
     newstyle <- khat(as.points(cardiff), cardiff$poly, s, newstyle=TRUE)
     str(newstyle)
     newstyle
     apply(newstyle$khats, 2, sum)
     plot(newstyle)

