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?
With thanks in advance,
Vincent Vinh-Hung
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