kinhat             package:spatialkernel             R Documentation

_I_n_h_o_m_o_g_e_n_e_o_u_s _K-_f_u_n_c_t_i_o_n _E_s_t_i_m_a_t_i_o_n

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

     Estimate the inhomogeneous K function of a non-stationary point
     pattern.

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

       kinhat(pts, lambda, poly, s)

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

     pts: matrix of the 'x,y'-coordinates of the point locations.

  lambda: intensity function evaluated at the above point locations.

    poly: matrix of the 'x,y'-coordinates of the polygon boundary.

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

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

     The inhomogeneous K function is a generalization of the usual K
     function defined for a second-order intensity-reweighted
     stationary point process, proposed by Baddeley _et al_ (2000). 

     When the true intensity function is unknown, and is to be
     estimated from the same data as been used to estimate the K
     function, a modified kernel density estimation implemented in
     'lambdahat' with argument 'gpts=NULL' can be used to calculate the
     estimated intensity at data points. See Baddeley _et al_ (2000)
     for details, and Diggle, P.J., _et al_ (2006) for a cautious note.

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

     A list with components 

       k: values of estimated K at the distances 's'.

       s: copy of 's'.

_N_o_t_e:

     This code is adapted from 'splancs' (Rowlingson and Diggle, 1993)
     fortran code for the estimation of homogeneous K function 'khat',
     with edge correction inherited for a general polygonal area.

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

        1.  Baddeley, A. J. and M{\o}ller, J. and Waagepetersen R.
           (2000) Non and semi-parametric estimation of interaction in 
           inhomogeneous point patterns, _Statistica Neerlandica_,
           *54*,  3, 329-350.

        2.  Diggle, P.J., V. Gacute{mathrm{o}}mez-Rubio, P.E. Brown,
           A.G. Chetwynd and S. Gooding (2006) Second-order analysis of
           inhomogeneous spatial point processes using case-control
           data, _submitted to Biometrics_.

        3.  Rowlingson, B. and Diggle, P. (1993) Splancs: spatial point
           pattern  analysis code in S-Plus.  _Computers and
           Geosciences_, *19*,  627-655.

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

     'khat', 'lambdahat'

