VVm {UCS} R Documentation

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

Description

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

Usage

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

Arguments

 `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

Details

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)]).

Value

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

References

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.

`zm`, `fzm`, `VVm`, `EV`, `EVm`