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Lyapunov Condition

If the third Moment exists for a Distribution of $x_i$ and the Lebesgue Integral is given by

\begin{displaymath}
{r_n}^3 =\sum_{i=1}^n \int_{-\infty}^\infty \vert x\vert^3\,dF_i(x),
\end{displaymath}

then if

\begin{displaymath}
\lim_{n\to\infty} {r_n\over s_n}=0,
\end{displaymath}

the Central Limit Theorem holds.

See also Central Limit Theorem




© 1996-9 Eric W. Weisstein
1999-05-25