## 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.

### See Also

`zm`

, `fzm`

, `VVm`

,
`EV`

, `EVm`

[Package

*UCS* version 0.5

Index]