In function logkda.R(), Boolean, with default
TRUE meaning to use Brobdingnagian numbers for the
calculation. This is slower but allows one to analyze larger
datasets
numerical
In function logkda.pari(), Boolean, with
default TRUE meaning to return a numerical vector and
FALSE meaning to return the string produced by
pari/gp
method
In function logkda(), a string specifying which
method to use. Takes R, a11, or pari
...
In function logkda(), further arguments which are
passed to the other functions
Details
The user should use function logkda(), which is a wrapper for
the other functions. Note that the default method, pari,
requires the pari/gp system to be installed. This is the preferred
option because it is much faster than the other methods.
Functions logkda.R() and logkda.pari() calculate
$K(D,A)$ using the method appearing in Etienne (2005), supplementary
online material; they use R and pari/gp respectively.
Function logkda.a11 is a direct implementation of formula A11
in Etienne (2005). The formula is
$$K(D,A)=
\sum_{\left{a_1,\ldots,a_S|\sum a_i=A\right}}
\prod_{i=1}^S\frac{
\overline{s}\left(n_i, a_i\right)
\overline{s}\left(a_i, 1\right) }{
\overline{s}\left(n_i,1\right)}$$
where $\overline{s}\left(n_i,a_i\right)$ are Stirling numbers of
the first kind (see logS1).
References
R. S. Etienne 2005. A New Sampling Formula for Neutral
Biodiversity. Ecology Letters, volume 8, pp253--260.
doi: 10.111/j.1461-0248.2004.00717.x
C. Batut and K. Belabas and D. Bernardi and H. Cohen and M. Olivier
2000. User's guide to PARI/GP. http://www.parigp-home.de/
a <- count(c(dogs=7,pigs=3,crabs=1,hogs=1,slugs=1))
logkda(a)
logkda.R(a)
logkda.R(a, use.brob=FALSE)
logkda.a11(a)
# All four should be the same up to numerical errors