EVm {UCS} | R Documentation |

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.

[Package *UCS* version 0.5 Index]