A sharp uniform bound for the distribution of a sum of Bernoulli random variables

Details A sharp uniform bound for the distribution of a sum of Bernoulli random variables A sharp uniform bound for the distribution of a sum of Bernoulli random variables

2008-06-13

arxiv.org/abs/0806.2350v1

Mathematics

Probability

Scientific paper

We establish a uniform bound for the distribution of a sum $S^n=X_1+...+X_n$
of independent non-homogeneous Bernoulli random variables with $P(X_i=1)=p_i$.
Specifically, we prove that $\sigma^n P(S^n=i)\leq M$ where $\sigma^n$ denotes
the standard deviation of $S^n$ and the constant $M~0.4688$ is the maximum of
$u\mapsto\sqrt{2u} e^{-2u}\sum_{k=0}^\infty({u^k\over k!})^2$.

Affiliated with

Also associated with

No associations

Rating

A sharp uniform bound for the distribution of a sum of Bernoulli random variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A sharp uniform bound for the distribution of a sum of Bernoulli random variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A sharp uniform bound for the distribution of a sum of Bernoulli random variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-494830