EVm                   package:UCS                   R Documentation

_E_x_p_e_c_t_e_d _F_r_e_q_u_e_n_c_y _S_p_e_c_t_r_u_m _o_f _a _L_N_R_E _M_o_d_e_l (_z_m, _f_z_m)

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

     Computes the expected frequency spectrum, relative frequency
     spectrum, and conditional parameter distribution of a LNRE model
     (Baayen, 2001) at sample size N.

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

     EVm(model, m, N, rho=1, relative=FALSE, ratio=FALSE, lower=TRUE)

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

   model: an object of class '"zm"' or '"fzm"', representing a
          Zipf-Mandelbrot (ZM) or finite Zipf-Mandelbrot (fZM) LNRE
          model

       m: a vector of positive integers, representing frequency ranks

       N: a vector of positive integers, representing sample sizes;
          either 'm' or 'N' should be a single number

     rho: a vector of numbers in the range [0,1].  If 'length(rho) >
          1', both 'm' and 'N' should be single numbers.  See below for
          details.

relative: if 'TRUE', computes the relative frequency spectrum (see
          below for details)

   ratio: if 'TRUE', computes the ratio between consecutive elements in
          the expected frequency spectrum

   lower: if 'rho' is specified, controls whether the lower or upper
          conditional parameter distribution is computed

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

     The expected frequency spectrum consists of the numbers E[V_m(N)],
     which stand for the expected number of types in frequency class m
     at sample size N, according to the LNRE model 'model' (see Baayen,
     2001).

     If 'relative=TRUE', the relative frequency spectrum E[V_m(N)] /
     E[V(N)] is returned.  If 'ratio=TRUE', the ratios between
     consecutive expected class sizes, E[V_{m+1}(N)] / E[V_m(N)], are
     returned.

     When 'rho' is specified, the conditional parameter distribution
     E[V_{m,rho}(N)] is returned, i.e. the expected number of types in
     frequency class m at sample size N with probability parameter pi
     <= rho.  If 'relative=TRUE', the expected proportion E[R_{m,rho}]
     approx E[V_{m,rho}(N)] / E[V(N)] is returned instead.  With
     'lower=FALSE', computes the upper conditional parameter
     distribution E[V_{m,>rho}(N)] or proportion E[R_{m,>rho}(N)]. See
     Evert (2004, Ch. 4) for details.

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

     a numeric vector of appropriate length (determined either by 'm',
     'N', or 'rho')

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

     Baayen, R. Harald (2001). _Word Frequency Distributions._ Kluwer,
     Dordrecht.

     Evert, Stefan (2004). _The Statistics of Word Cooccurrences: Word
     Pairs and Collocations._ PhD Thesis, IMS, University of Stuttgart.

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

     'zm', 'fzm', 'EVm', 'VV', 'VVm'

