pcf                 package:spatstat                 R Documentation

_P_a_i_r _C_o_r_r_e_l_a_t_i_o_n _F_u_n_c_t_i_o_n

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

     Estimate the pair correlation function.

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

      pcf(X, ...)

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

       X: Either the observed data point pattern, or an estimate of its
          K function, or an array of multitype K functions (see
          Details). 

     ...: Other arguments passed to the appropriate method. 

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

     The pair correlation function of a stationary point process is

                     g(r) = K'(r)/ ( 2 * pi * r)

     where K'(r) is the derivative of K(r), the reduced second moment
     function (aka ``Ripley's K function'') of the point process. See
     'Kest' for information about K(r). For a stationary Poisson
     process, the pair correlation function is identically equal to 1.
     Values g(r) < 1 suggest inhibition between points; values greater
     than 1 suggest clustering.

     We also apply the same definition to other variants of the
     classical K function, such as the multitype K functions (see
     'Kcross', 'Kdot') and the inhomogeneous K function (see 'Kinhom').
     For all these variants, the benchmark value of K(r) = pi * r^2
     corresponds to g(r) = 1.

     This routine computes an estimate of g(r) either directly from a
     point pattern, or indirectly from an estimate of K(r) or one of
     its variants.

     This function is generic, with methods for the classes '"ppp"',
     '"fv"' and '"fasp"'.

     If 'X' is a point pattern (object of class '"ppp"') then the pair
     correlation function is estimated using a traditional kernel
     smoothing method (Stoyan and Stoyan, 1994). See 'pcf.ppp' for
     details.

     If 'X' is a function value table (object of class '"fv"'), then it
     is assumed to contain estimates of the K function or one of its
     variants (typically obtained from 'Kest' or 'Kinhom'). This
     routine computes an estimate of g(r)  using smoothing splines to
     approximate the derivative. See 'pcf.fv' for details.

     If 'X' is a function value array (object of class '"fasp"'), then
     it is assumed to contain estimates of several K functions
     (typically obtained from 'Kmulti' or 'alltypes'). This routine
     computes an estimate of g(r) for each cell in the array, using
     smoothing splines to approximate the derivatives. See 'pcf.fasp'
     for details.

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

     Either a function value table (object of class '"fv"', see
     'fv.object') representing a pair correlation function, or a
     function array (object of class '"fasp"', see 'fasp.object')
     representing an array of pair correlation functions.

_A_u_t_h_o_r(_s):

     Adrian Baddeley adrian@maths.uwa.edu.au <URL:
     http://www.maths.uwa.edu.au/~adrian/> and Rolf Turner
     rolf@math.unb.ca <URL: http://www.math.unb.ca/~rolf>

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

     Stoyan, D. and Stoyan, H. (1994) Fractals, random shapes and point
     fields: methods of geometrical statistics. John Wiley and Sons.

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

     'pcf.ppp', 'pcf.fv', 'pcf.fasp', 'Kest', 'Kinhom', 'Kcross',
     'Kdot', 'Kmulti', 'alltypes'

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

       # ppp object
       data(simdat)
       
       p <- pcf(simdat)
       plot(p)

       # fv object
       K <- Kest(simdat)
       p2 <- pcf(K)
       plot(p2)

       # multitype pattern; fasp object
       data(betacells)
       
       p <- pcf(alltypes(betacells, "K"))
       plot(p)

