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)
     print.khat(x, ...)
     plot.khat(x, ...)

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

     pts: A points data set 

    poly: A polygon containing the points 

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

newstyle: if TRUE, the function returns a khat object

       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 <oedic@cebc.cnrs.fr> 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)

