Vincent Vinh-Hung wrote:
> General question,
> I've seen two descriptions of "logarithmic distribution".
> One is related to the frequency of digits called Benford's law (digit 1
> occurs more frequently than 2, 2 than 3, etc) whose explanation is that
> it is the result of a mixture of distributions.
> The other description is a 2-page paragraph The logarithmic distribution
> in Kendall and Stuart (1977, The Advanced theory of statistics, Vol 1,
> 4th edition, pp 139-140), attributing the derivation to Fisher (1943).
> Are these concepts of logarithmic distribution the same or not?
>
> Second question I would like to ask: Kendall and Stuart give an
> example of a distribution of the logarithmic type from Fisher (1943),
> "distribution of butterflies in Malaya, with theoretical frequencies
> given by the logarithmic distribution"
> No. of species Theoretical frequency Observed frequency
> 1 135.05 118
> 2 67.33 74
> 3 44.75 44
> 4 33.46 24
> 5 26.69 29
> 6 22.17 22
> 7 18.95 20
> etc ...
> From what I've understood, the theoretical frequency was generated
> by
> - ( q^r ) / ( r * ln(1-q) )
> in which r is the No. of species, q is the probability of the presence
> of an attribute.
> How was, how can the fit be realized?
You will need a value of q first. This will either be estimated from the raw
data or assumed by some hypothesis. Once you have this just plug in the
value of r you want and multiply the resulting probability by the sum of
the observed frequencies.
You might also be able to use the theorectical mean q/((q - 1 )*Log[1 - q])
to estimate q by equating it to the sample mean and solving for q.
>
>
> With thanks in advance,
> Vincent Vinh-Hung
--
Dr Graeme Byrne
La Trobe University, Bendigo
PO Box 199, Bendigo, 3552
Phone: 61 3 5444 7263
Fax: 61 3 5444 7998
[EMAIL PROTECTED]
===========================================================================
This list is open to everyone. Occasionally, less thoughtful
people send inappropriate messages. Please DO NOT COMPLAIN TO
THE POSTMASTER about these messages because the postmaster has no
way of controlling them, and excessive complaints will result in
termination of the list.
For information about this list, including information about the
problem of inappropriate messages and information about how to
unsubscribe, please see the web page at
http://jse.stat.ncsu.edu/
===========================================================================
