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Le Cam's Inequality

Let S_n be the sum of n random variates X_i with a Bernoulli distribution with P(X_i=1)=p_i. Then

sum_(k=0)^infty|P(S_n=k)-(e^(-lambda)lambda^k)/(k!)|<2sum_(i=1)^np_i^2,

where

lambda=sum_(i=1)^np_i.

See also

Bernoulli Distribution

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References

Le Cam, L. "An Approximation Theorem for the Poisson Binomial Distribution." Pacific J. Math. 10, 1181-1197, 1960.Le Cam, L. "On the distribution of Sums of Independent Random Variables." In Bernoulli, Bayes, Laplace: Proceeding of an International Research Seminar (Ed. J. Neyman and L. M. Le Cam). New York: Springer-Verlag, pp. 179-202, 1963.Steele, J. M. "Le Cam's Inequality." Amer. Math. Monthly 101, 48-54, 1994.

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Le Cam's Inequality

Cite this as:

Weisstein, Eric W. "Le Cam's Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LeCamsInequality.html

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