EVm {UCS}R Documentation

Expected Frequency Spectrum of a LNRE Model (zm, fzm)


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


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


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


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, EVm, VV, VVm

[Package UCS version 0.5 Index]