quadrat count indices: program almost ready

[Darrell McCauley]

I've written a little program to calculate quadrat count
indices (See Cressie, _Statistics for Spatial Data_,
pp 590-591, 1st ed, Wiley & Sons, 1991). Sample 
output is attached.

If you know what I'm talking about here and/or
think that something like this would be useful
in GRASS, I need your assistance. The grass program,
man page, and tutorial is all ready to be distributed
except for one small problem: Morista's I. The formula
given in Cressie's book (1st ed - I couldn't afford the 
2nd after buying the first :(  ) gives Morista's I as

\begin{displaymath}     % please bear with the TeX-ease
I_\delta = \frac{\sum_{i=1}^n X_i\left(X_i-1\right)}
                {n\bar{X}\left(n\bar{X}-1\right)}
\end{displaymath}% \bar{X}=mean, X_i=#sites in ith quadrat, n=#quadrats

However, this equation gave me answers that were an order
of magnitude lower that Cressie's example calculation in Table 8.3.
By altering the equation to be:

\begin{displaymath}
I_\delta = \frac{\sum_{i=1}^n X_i\left(X_i-1\right)}
                {\bar{X}\left(n\bar{X}-1\right)}
\end{displaymath}

I get an answer that appears more correct (notice the n is 
missing from the denominator.)

Which is correct - Cressie's equation or his calculation?  (Or which
equation is correct - the printed one or the altered one?)  If someone
can pull a book (Ripley?) off their shelf and check I'll make the program
available.  It's too dern cold (zero farenheit) to make a special trip
to the library for this :-)

--Darrell

> % s.qcount -q sites=pinetrees
> Index                                   Realization
> -----------------------------------------------------------
> Fisher el al (1922) Relative Variance            2.12795
> David & Moore (1954) Index of Cluster Size       1.12795
> Douglas (1975) Index of Cluster Frequency        1.38304
> Lloyd (1967) "mean crowding"                     2.68795
> Lloyd (1967) Index of patchniess                 1.72304
> Morita's (1959) I (variability b/n patches)      1.72043
> -----------------------------------------------------------
> sites_list: pinetrees n=584 (100 quadrats of radius 6)

(also prints raw quadrat counts as a site list with an
optional flag)