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Logarithmic Distribution

A Continuous Distribution for a variate with probability function

\begin{displaymath}
P(x)={\log x\over b(\log b-1)-a(\log a-1)}
\end{displaymath}

and distribution function

\begin{displaymath}
D(x)={a(1-\log a)-x(1-\log x)\over a(1-\log a)-b(1-\log b)}.
\end{displaymath}

The Mean is

\begin{displaymath}
\mu={a^2(1-2\log a)-b^2(1-2\log b)\over 4[a(1-\log a)-b(1-\log b)]},
\end{displaymath}

but higher order moments are rather messy.




© 1996-9 Eric W. Weisstein
1999-05-25