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)

