VVm                   package:UCS                   R Documentation

_V_a_r_i_a_n_c_e_s _o_f _t_h_e _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 variances of the frequency spectrum and conditional
     parameter distribution of a LNRE model (Baayen, 2001) at sample
     size N.

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

     VVm(model, m, N, rho=1, relative=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 variances for the relative conditional
          parameter distribution (see below for details).  May only be
          used when 'rho' is specified.

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

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

     The variance V[V_m(N)] is computed according to Baayen (2001,
     120f).  

     When 'rho' is specified, the variances of the conditional
     parameter distribution V[V_{m,rho}(N)] or the corresponding
     proportions V[R_{m,rho}(N)] are returned, depending on the value
     of 'relative'.  With 'lower=FALSE', computes variances for the
     upper conditional parameter distribution V[V_{m,>rho}(N)] or
     proportion V[R_{m,>rho}(N)]. See Evert (2004, Ch. 4) for details.

     The 'EVm' help page provides more information about V_m(N),
     V_{m,rho}(N), R_{m,rho}(N), V_{m,>rho}(N) and R_{m,>rho}(N).

     Note that this function does _not_ compute variances for the
     relative frequency spectrum (V[V_m(N)/V(N)]) or the ratio between
     consecutive spectrum elements (V[V_{m+1}(N)/V_m(N)]).

_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', 'VVm', 'EV', 'EVm'

