khvc                 package:splancs                 R Documentation

_C_o_v_a_r_i_a_n_c_e _m_a_t_r_i_x _f_o_r _t_h_e _d_i_f_f_e_r_e_n_c_e _b_e_t_w_e_e_n _t_w_o _K-_f_u_n_c_t_i_o_n_s

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

     Calculate the covariance matrix for the difference between two
     K-functions. Also return the contribution to the variance for each
     of the two point patterns,

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

     khvc(pts1, pts2, poly, s)

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

    pts1: An object containing the case locations. 

    pts2: An object containing the control locations. 

    poly: A polygon enclosing the locations in 'pts1' and 'pts2' 

       s: A vector of distances at which the calculation is to be made. 

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

     A list with four components: 

  varmat: The upper triangle of the covariance matrix.

     k11: The variance of Khat for the cases

     k22: The variance of Khat for the controls

     k12: The covariance of Khat for the cases and Khat for controls.

_N_o_t_e:

     Note that the diagonal of the covariance matrix is '$k11 - 2 *
     $k12 + $k22 '

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

     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:

     'khat', 'khvmat', 'secal'

