power.law.fit             package:igraph             R Documentation

_F_i_t_t_i_n_g _a _p_o_w_e_r-_l_a_w _d_i_s_t_r_i_b_u_t_i_o_n _f_u_n_c_t_i_o_n _t_o _d_i_s_c_r_e_t_e _d_a_t_a

_D_e_s_c_r_i_p_t_i_o_n:

     'power.law.fit' fits a power-law distribution to a data set.

_U_s_a_g_e:

     power.law.fit(x, xmin = NULL, start = 2, ...)

_A_r_g_u_m_e_n_t_s:

       x: The data to fit, a numeric vector containing integer values.

    xmin: The lower bound for fitting the power-law. If NULL, the
          smallest value in 'x' will be used. This argument makes it
          possible to fit only the tail of the distribution. 

   start: The initial value of the exponent for the minimizing
          function. Ususally it is safe to leave this untouched.

     ...: Additional arguments, passed to the maximum likelyhood
          optimizing function, 'mle'.

_D_e_t_a_i_l_s:

     A power-law distribution is fitted with maximum likelyhood methods
     as recommended by Newman and (by default) the  BFGS optimization
     (see mle) algorithm is applied.

     The additional arguments are passed to the mle function, so it is
     possible to change the optimization method and/or its parameters.

_V_a_l_u_e:

     An object with class ''mle''. It can be used to calculate
     confidence intervals and log-likelihood. See 'mle-class' for
     details.

_A_u_t_h_o_r(_s):

     Gabor Csardi csardi@rmki.kfki.hu

_R_e_f_e_r_e_n_c_e_s:

     Power laws, Pareto distributions and Zipf's law, M. E. J. Newman,
     _Contemporary Physics_, in press.

_S_e_e _A_l_s_o:

     'mle'

_E_x_a_m_p_l_e_s:

     # This should approximately yield the correct exponent 3
     g <- barabasi.game(1000)    # increase this number to have a better estimation
     d <- degree(g, mode="in")
     power.law.fit(d+1, 20)

