k12hat                package:splancs                R Documentation

_B_i_v_a_r_i_a_t_e _K-_f_u_n_c_t_i_o_n

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

     Calculates an estimate of the bivariate K-function

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

     k12hat(pts1,pts2,poly,s)

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

pts1,pts2: Two points data sets 

    poly: A polygon containing the points 

       s: A vector of distances at which to estimate the K12 function 

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

     The bivariate K function is defined as the expected number of
     points of pattern 1 within a distance s of an arbitrary point of
     pattern 2, divided by the overall density of the points in pattern
     1.  To estimate this function, the approximately unbiased
     estimator given by Lotwick and Silverman (1982) is used.

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

     A vector like 's' containing the value of K12hat at the points in
     's'.

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

     Lotwick, H.W. and Silverman B.W. (1982) Methods for Analysing
     Spatial Processes of Several types of Points. _J. R. Statist Soc_
     B44 406-13; 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.

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

     data(okwhite)
     data(okblack)
     okpoly <- list(x=c(okwhite$x, okblack$x), y=c(okwhite$y, okblack$y))
     plot(seq(5,80,5), sqrt(k12hat(as.points(okwhite), as.points(okblack), 
     bbox(as.points(okpoly)), seq(5,80,5))/pi) - seq(5,80,5), xlab="distance", 
     ylab=expression(hat(L)[12]), ylim=c(-20,20), type="l")

