Strengthened bounds for the probability of k-out-of-n events

Given a set of n random events in a probability space, represented by n Bernoulli variables, we consider the probability that k out of n events occur. When partial distribution information, i.e., moments up to level m (m < n,) is provided, only an upper or lower bound can be computed for this probability. Pr´ekopa and Gao [9] proposed a polynomial-size linear program to obtain such bounds. In this paper, we propose inequalities that can be added to this linear program to strengthen the bounds. We present numerical examples that demonstrate the potential of these new inequalities.

• Type: Journal
• Year: 2016
• Where: DAM
• Authors: Feng Qiu, Shabbir Ahmed, Santanu S. Dey
• Keywords: DAM 2016