Lc                   package:ineq                   R Documentation

_L_o_r_e_n_z _C_u_r_v_e

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

     computes the (empirical) ordinary and generalized Lorenz curve of
     a vector x

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

     Lc(x, n=rep(1,length(x)), plot=F) 

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

       x: a vector containing non-negative elements

       n: a vector of frequencies, must be same length as `x'

    plot: logical flag. If TRUE the empirical Lorenz curve will be
          plotted

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

     `Lc(x)' computes the empirical ordinary Lorenz curve of `x' as
     well as the generalized Lorenz curve (= ordinary Lorenz curve *
     mean(x)). the result can be interpreted like this: `p'*100 percent
     have `L(p)'*100 percent of `x'.

     if `n' is changed to anything but the default `x' is interpreted
     as a vector of class means and `n' as a vector of class
     frequencies: in this case `Lc' will compute the minimal Lorenz
     curve (= no inequality within each group). a maximal curve can be
     computed with `Lc.mehran'.

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

     a list with the following components: 

       p: vector of percentages

       L: vector with values of the ordinary Lorenz curve

L.general: vector with values of the generalized Lorenz curve

_A_u_t_h_o_r(_s):

     Achim Zeileis zeileis@ci.tuwien.ac.at

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

     B C Arnold: Majorization and the Lorenz Order: A Brief
     Introduction, 1987, Springer,

     F A Cowell: Measurement of Inequality, 2000, in A B Atkinson / F
     Bourguignon (Eds): Handbook of Income Distribution, Amsterdam, 

     F A Cowell: Measuring Inequality, 1995 Prentice Hall/Harvester
     Wheatshef.

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

     `Lc.plot', `Lc.mehran', `theor.Lc.plot'

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

     # income distribution of the USA in 1968 (in 10 classes)
     # x vector of class means, n vector of class frequencies
     x <- c(541, 1463, 2445, 3438, 4437, 5401, 6392, 8304, 11904, 22261)
     n <- c(482, 825, 722, 690, 661, 760, 745, 2140, 1911, 1024)

     # compute minimal Lorenz curve (= no inequality in each group)
     Lc.min <- Lc(x, n=n)
     # compute maximal Lorenz curve (limits of Mehran)
     Lc.max <- Lc.mehran(x,n)
     # plot both Lorenz curves in one plot                        
     Lc.plot(Lc.min)
     Lc.plot(Lc.max, new=T, col=4)

     # add the theoretic Lorenz curve of a Lognormal-distribution with (var=0.78)
     theor.Lc.plot(type="lognorm", parameter=0.78)
     # add the theoretic Lorenz curve of a Dagum-distribution
     theor.Lc.plot(type="Dagum", parameter=c(3.4,2.6))

