Let
be a set of Independent random variates and each
have an arbitrary probability distribution
with Mean and a finite Variance
. Then the normal form variate
(1) |
(2) |
(3) |
|
(4) |
(5) |
(6) |
(7) |
(8) | |||
(9) |
(10) |
(11) |
(12) |
(13) |
(14) |
The ``fuzzy'' central limit theorem says that data which are influenced by many small and unrelated random effects are approximately Normally Distributed.
See also Lindeberg Condition, Lindeberg-Feller Central Limit Theorem, Lyapunov Condition
References
Abramowitz, M. and Stegun, C. A. (Eds.).
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, 1972.
Spiegel, M. R. Theory and Problems of Probability and Statistics.
New York: McGraw-Hill, pp. 112-113, 1992.
Zabell, S. L. ``Alan Turing and the Central Limit Theorem.'' Amer. Math. Monthly 102, 483-494, 1995.
© 1996-9 Eric W. Weisstein