1990/04/01 by András Prékopa · 2 citations
Computer Science · Mathematics · #Applied mathematics #Basis (linear algebra) #Bayesian Modeling and Causal Inference #Binomial (polynomial) #Binomial theorem #Combinatorics #Complexity and Algorithms in Graphs #Discrete mathematics #Dual (grammatical number) #Formal Methods in Verification #Inequality #Linear inequality #Linear programming #Mathematical analysis #Mathematical optimization #Mathematics #Statistics #Upper and lower bounds
paper · doi:10.1287/opre.38.2.227
openalex publication_date 1990/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25
In a previous paper (1988), the author proposed methods to obtain sharp lower and upper bounds for probabilities that at least one out of n events occurs, based on the knowledge of some of the binomial moments of the number of events which occur and linear programming formulations. This paper presents further results concerning other and more general logical functions of events: We give sharp lower and upper bounds for the probabilities that: a) exactly r events, b) at least r events occur, using linear programming. The basic facts are expressed by the dual feasible basis characterization theorems which are interpreted in terms of the vertices of the dual problems. We mention some linear inequalities, among the binomial moments, generalize the theory for the case of nonconsecutive binomial moments and present numerical examples.