VVm {UCS}R Documentation

Variances of the Frequency Spectrum of a LNRE Model (zm, fzm)


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


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


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


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

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


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


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.

See Also

zm, fzm, VVm, EV, EVm

[Package UCS version 0.5 Index]