ripras               package:spatstat               R Documentation

_E_s_t_i_m_a_t_e _w_i_n_d_o_w _f_r_o_m _p_o_i_n_t_s _a_l_o_n_e

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

     Given an observed pattern of points, computes the Ripley-Rasson
     estimate of  the spatial domain from which they came.

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

      ripras(x, y=NULL)

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

       x: vector of 'x' coordinates of observed points, or a 2-column
          matrix giving 'x,y' coordinates, or a list with components
          'x,y' giving coordinates.

       y: (optional) vector of 'y' coordinates of observed points, if
          'x' is a vector.

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

     Given an observed pattern of points with coordinates  given by 'x'
     and 'y', this function computes  an estimate due to Ripley and
     Rasson (1977) of the spatial domain from which the points came. 

     The points are assumed to have been generated independently and
     uniformly distributed inside an unknown domain D. The maximum
     likelihood estimate of D is the convex hull of the  points.
     Analogously to the problems of estimating the endpoint of a
     uniform distribution, the MLE is not optimal. Ripley and Rasson's
     estimator is a rescaled copy of the convex hull, centred at the
     centroid of the convex hull. The scaling factor is  1/sqrt{1 -
     frac m n} where n is the number of data points and  m the number
     of vertices of the convex hull.

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

     A window (an object of class '"owin"').

_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:

     Ripley, B.D. and Rasson, J.-P. (1977) Finding the edge of a
     Poisson forest. _Journal of Applied Probability_, *14*, 483 - 491.

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

     'owin', 'as.owin'

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

       ## Not run: 
       plot(owin())
       
     ## End(Not run)
       x <- runif(30)
       y <- runif(30)
       ## Not run: points(x,y)
       w <- ripras(x,y)
       ## Not run: 
       plot(w, box=FALSE)
       points(x,y)
       
     ## End(Not run)

