Fzero                package:splancs                R Documentation

_T_h_e_o_r_e_t_i_c_a_l _n_e_a_r_e_s_t _n_e_i_g_h_b_o_u_r _d_i_s_t_r_i_b_u_t_i_o_n _f_u_n_c_t_i_o_n

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

     Calculate the theoretical nearest neighbour distribution function.

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

     Fzero(density,s)

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

 density: The density of the point pattern, i.e. the number of points
          per unit area. 

       s: A vector of distances at which to evaluate Fzero 

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

     Fzero returns the nearest neighbour distribution for a homogeneous
     planar Poisson process. In fortran notation, Fzero(s) is 'FZERO =
     1-EXP(-PI*DENSITY*(S**2))'.

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

     A vector of the same length as 's', containing the value of Fzero
     at the  distances in 's'.

_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:

     'Fhat','Ghat','pdense'

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

     data(uganda)
     plot(Ghat(as.points(uganda), seq(20, 500, 20)), Fzero(pdense(as.points(uganda), 
     uganda$poly), seq(20, 500, 20)), type="l", ylab="Theoretical G", 
     xlab="Estimated G")
     lines(c(0,1),c(0,1),lty=2)

