EVm {UCS} R Documentation

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

### Description

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

### Usage

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

### Details

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.

### 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`, `EVm`, `VV`, `VVm`