Logarithmic Distribution
K ~ Logarithmic(p)
Species-Abundance / Compound-Poisson Family • Published August 10, 2026
Fisher's 1943 species-abundance model: history from Fisher, Corbet, and Williams's moth-trapping data at Rothamsted, the first discrete sheet in this series with support starting at 1 rather than 0, an exact compound-Poisson tie showing this is precisely the 'jump size' distribution hiding inside the already-published Negative Binomial, a maximum-likelihood equation with no closed form solved by one-dimensional root-finding, and direct simulation via NumPy's dedicated logseries generator.
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About This Reference Sheet
Fisher's 1943 species-abundance model: history from Fisher, Corbet, and Williams's moth-trapping data at Rothamsted, the first discrete sheet in this series with support starting at 1 rather than 0, an exact compound-Poisson tie showing this is precisely the 'jump size' distribution hiding inside the already-published Negative Binomial, a maximum-likelihood equation with no closed form solved by one-dimensional root-finding, and direct simulation via NumPy's dedicated logseries generator.
Support
k ∈ {1, 2, 3, ...}
Parameters
p ∈ (0, 1)