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Date: 3-5-2021
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The Lyapunov condition, sometimes known as Lyapunov's central limit theorem, states that if the th moment (with ) exists for a statistical distribution of independent random variates (which need not necessarily be from same distribution), the means and variances are finite, and
(1) |
then if
(2) |
where
(3) |
the central limit theorem holds.
REFERENCES:
Ash, R. B. and Doléans-Dade, C. A. Probability & Measure Theory, 2nd ed. New York: Academic Press, p. 307, 1999.
Billingsley, P. Probability and Measure, 2nd ed. New York: p. 371, Wiley, 1986.
Resnik, S. A Probability Path. Boston, MA: Birkhäuser, p. 319, 1999.
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