logkda
Etienne's K(D,A)
Calculates Etienne's $K(D,A)$ using a variety of different methods
- Keywords
- math
Usage
logkda.R(a, use.brob=TRUE)
logkda.a11(a)
logkda.pari(a, numerical=TRUE)
logkda(a, method="pari", ...)Arguments
- a
- Count object
- use.brob
- In function
logkda.R(), Boolean, with defaultTRUEmeaning to use Brobdingnagian numbers for the calculation. This is slower but allows one to analyze larger datasets - numerical
- In function
logkda.pari(), Boolean, with defaultTRUEmeaning to return a numerical vector andFALSEmeaning to return the string produced bypari/gp - method
- In function
logkda(), a string specifying which method to use. TakesR ,a11 , orpari - ...
- 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).
Note
If method takes its default value of paripari/gp is not installed (the test is gp --version),
then the method is changed to R and a warning given.
Function logkda.a11() is included because the computational
method is a direct transcription of formula A11; it is very slow.
It would be nice to use gp2c (rather than gp) but I
can't make the -ggp2c-run to make it call gp with the -q
flag
References
R. S. Etienne 2005. doi: 10.111/j.1461-0248.2004.00717.x
C. Batut and K. Belabas and D. Bernardi and H. Cohen and M. Olivier
2000.
See Also
Examples
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