Extremal distributions for tail probabilities of sums of iid random variables on [0,1]

Details Extremal distributions for tail probabilities of sums of iid random variables on [0,1] Extremal distributions for tail probabilities of sums of iid random variables on [0,1]

2008-08-12

arxiv.org/abs/0808.1669v1

Mathematics

Probability

Scientific paper

Two old conjectures from problem sections, one of which from SIAM Review, concern the question of finding distributions that maximize P(Sn <= t), where Sn is the sum of i.i.d. random variables X1, ..., Xn on the interval [0,1], satisfying E[X1]=m. In this paper a Lagrange multiplier technique is applied to this problem, yielding necessary conditions for distributions to be extremal, for arbitrary n. For n=2, a complete solution is derived from them: extremal distributions are discrete and have one of the following supports, depending on m and t: {0,t}, {t-1,1}, {t/2,1}, or {0,t,1}. These results suffice to refute both conjectures. However, acquired insight naturally leads to a revised conjecture: that extremal distributions always have at most three support points and belong to a (for each n, specified) finite collection of two and three point distributions.

Affiliated with

Also associated with

No associations

Rating

Extremal distributions for tail probabilities of sums of iid random variables on [0,1] 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 Extremal distributions for tail probabilities of sums of iid random variables on [0,1], we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Extremal distributions for tail probabilities of sums of iid random variables on [0,1] will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-202960