The exact evaluation of the Poisson and Binomial cumulative distribution and inverse (quantile) functions may be too challenging\r\nor unnecessary for some applications, and simpler solutions (typically obtained by applying Normal approximations or exponential\r\ninequalities) may be desired in some situations. Although Normal distribution approximations are easy to apply and potentially\r\nvery accurate, error signs are typically unknown; error signs are typically known for exponential inequalities at the expense of some\r\npessimism. In this paper, recent work describing universal inequalities relating the Normal and Binomial distribution functions is\r\nextended to cover the Poisson distribution function; new quantile function inequalities are then obtained for both distributions.\r\nExponential boundsââ?¬â?which improve upon the Chernoff-Hoeffding inequalities by a factor of at least twoââ?¬â?are also obtained for\r\nboth distributions.
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