theorLc                 package:ineq                 R Documentation

_T_h_e_o_r_e_t_i_c_a_l _L_o_r_e_n_z _C_u_r_v_e_s

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

     Theoretical Lorenz curves of income distributions

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

     theorLc(type=c("Singh-Maddala","Dagum","lognorm","Pareto","exponential"), parameter=0)

     Lc.dagum(p, parameter=c(2,2))
     Lc.singh(p, parameter=c(2,2))
     Lc.pareto(p, parameter=2)
     Lc.lognorm(p, parameter=1)
     Lc.exp(p)

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

    type: character string giving the income distribution. Must be one
          of the strings in the default argument (the first character
          is sufficient). Defaults to "Singh-Maddala".

parameter: vector containing parameter(s) of the distributions.

       p: vector with elements from [0,1].

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

     `Lc.dagum', `Lc.singh', `Lc.pareto', `Lc.lognorm', `Lc.exp' are
     theoretical Lorenz curves of income distributions. They are
     functions of class `"theorLc"' with plot- and a lines- method, so
     that they can be added into an existing Lorenz curve plot.

     `theorLc' returns a function of class `"theorLc"', that is a one
     of the above theoretical Lorenz curves with fixed parameters.

     `Lc.dagum' is the Lorenz curve of the Dagum distribution (2
     parameters), `Lc.singh' the one of the Singh-Maddala distribution
     (2 parameters), `Lc.pareto' the one of the Pareto distribution (1
     parameter), `Lc.lognorm' the one of the Lognormal distribution (1
     parameter) and `Lc.exp' the Lorenz curve of the exponential
     distribution (no parameter).

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

     A function of class `"theorLc"' or its value at `p' respectively.

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

     Achim Zeileis zeileis@ci.tuwien.ac.at

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

     C Dagum: Income Distribution Models, 1983, in: Johnson / Kotz
     (Eds): Encyclopedia of Statistical Sciences Vol.4, 27-34.

     J B McDonald: Some generalized functions for the size distribution
     of income, 1984, Econometrica 52, 647-664.

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

     `Lc', `plot.Lc', `plot.theorLc'

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

     ## Load and attach income (and metadata) set from Ilocos, Philippines
     data(Ilocos)
     attach(Ilocos)
     ## extract income for the province "Pangasinan"
     income.p <- income[province=="Pangasinan"]

     ## plot empirical Lorenz curve and add theoretical Lorenz curve of
     ## a lognormal distribution with an estimate of the standard
     ## deviation parameter
     Lc.p <- Lc(income.p)
     plot(Lc.p)
     lines(Lc.lognorm, parameter=sd(log(income.p)), col=4)


     # vector of percentages
     p <- (1:10)*0.1
     # compute values of theoretic Lorenz curve of a Dagum-distribution
     Lc.dagum(p, parameter=c(3.4,2.6))
     # or
     mydagum <- theorLc(type="Dagum", parameter=c(3.4,2.6))
     mydagum(p)

