Estimates for probabilities of independent events and infinite series
J\"urgen Grahl, Shahar Nevo
TL;DR
This paper derives sharp lower bounds for the probability of unions of independent events with given probabilities, providing insights applicable to infinite series in probability theory.
Contribution
It introduces new bounds for the union probability of independent events with specified probabilities, extending to infinite series.
Findings
Established sharp lower bounds for union probabilities
Extended results to infinite series of independent events
Provided theoretical tools for probability bounds in complex scenarios
Abstract
This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The results have parallel meanings in terms of infinite series.
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Taxonomy
TopicsReservoir Engineering and Simulation Methods · Statistical and Computational Modeling · Fault Detection and Control Systems