The constructor function lnre.fzm is not user-visible. It is
invoked implicitly when lnre is called with LNRE model type
"fzm".
lnre.fzm(alpha=.8, A=1e-9, B=.01, param=list()) ## user call: lnre("fzm", spc=spc) or lnre("fzm", alpha=.8, A=1e-9, B=.01)
$$\pi_k = \frac{C}{(k + b) ^ a}$$ for $k = 1, \ldots, S$. The parameters of the Zipf-Mandelbrot law are $a > 1$, $b \ge 1$ and $S$ (see also Baayen 2001, 101ff). The fZM model is given by the type density function
$$g(\pi) := C\cdot \pi^{-\alpha-1}$$
for $A \le \pi \le B$ (and $\pi = 0$ otherwise), and has three parameters $0 < \alpha < 1$ and $0 < A < B \le 1$. The normalizing constant is
$$C = \frac{ 1 - \alpha }{ B^{1 - \alpha} - A^{1 - \alpha} }$$
and the population vocabulary size is
$$S = \frac{1 - \alpha}{\alpha} \cdot \frac{ A^{-\alpha} - B^{-\alpha} }{ B^{1 - \alpha} - A^{1 - \alpha} }$$
See Evert (2004) and the lnre.zm manpage for further
details.
lnre.fzm(alpha=.5, A=5e-12, B=.1)
or as a list of name-value pairs:
lnre.fzm(param=list(alpha=.5, A=5e-12, B=.1))
which is usually more convenient when the constructor is invoked by
another function (such as lnre). If both immediate arguments
and the param list are given, the immediate arguments override
conflicting values in param. For any parameters that are
neither specified as immediate arguments nor listed in param,
the defaults from the function prototype are inserted.
The lnre.fzm constructor also checks the types and ranges of
parameter values and aborts with an error message if an invalid
parameter is detected.
NB: parameter estimation is faster and more robust for the
inexact fZM model, so you might consider passing the
exact=FALSE option to lnre unless you intend to make
predictions for small sample sizes $N$ and/or high spectrum elements
$E[V_m(N)]$ ($m \gg 1$) with the model.
Evert, Stefan (2004). A simple LNRE model for random character sequences. Proceedings of JADT 2004, 411-422.
lnre for pointers to relevant methods and functions for
objects of class lnre, as well as a complete listing of LNRE
models implemented in the zipfR library.