2013/12/23 by Michael Short · 1 citation
Physics and Astronomy · Decision Sciences · Engineering · #Scientific Research and Discoveries #Probabilistic and Robust Engineering Design #Diverse Scientific and Engineering Research
paper · pdf · doi:10.1155/2013/412958
openalex publication_date 2013/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
The exact evaluation of the Poisson and Binomial cumulative distribution and inverse (quantile) functions may be too challenging or unnecessary for some applications, and simpler solutions (typically obtained by applying Normal approximations or exponential inequalities) may be desired in some situations. Although Normal distribution approximations are easy to apply and potentially very accurate, error signs are typically unknown; error signs are typically known for exponential inequalities at the expense of some pessimism. In this paper, recent work describing universal inequalities relating the Normal and Binomial distribution functions is extended to cover the Poisson distribution function; new quantile function inequalities are then obtained for both distributions. Exponential bounds—which improve upon the Chernoff-Hoeffding inequalities by a factor of at least two—are also obtained for both distributions.