Abstract #301430

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JSM 2003 Abstract #301430
Activity Number: 447
Type: Contributed
Date/Time: Thursday, August 7, 2003 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #301430
Title: An Optimal Probability Lower Bound Strengthening the Dawson-Sankoff Bound
Author(s): Tuhao John Chen*+
Companies: Bowling Green State University
Address: Department of Math and Statistics, Bowling Green, OH, 43402,
Keywords: binomial moments ; Bonferroni-type bounds ; Dawson-Sankoff inequality ; Frechet optimality
Abstract:

We will discuss a lower bound for the probability that at least one out of n arbitrary events occurs. The information used is the first- and second- degree Bonferroni summations in conjunction with quantities A and B, where A is the probability that exactly one event occurs and B is the probability that exactly n events occur. We prove that the proposed bound is a Frechet optimal lower bound. Two additional nonnegative terms used in the proposed bound make it at least as good as the Dawson-Sankoff lower bound, which is an optimal degree two lower bound using the first- and second- degree Bonferroni summations. The newly constructed lower bound theoretically answers the question on the improvement of the degree two optimal lower bound. A numerical example is presented to illustrate that in some cases, the improvement can be very substantial.

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