Monotonicity properties of the Poisson approximation to the binomial distribution
Iosif Pinelis
TL;DR
This paper investigates the monotonicity properties of the Poisson approximation to the binomial distribution and applies these findings to develop exact hypothesis tests for the binomial parameter p.
Contribution
It establishes new monotonicity properties of the Poisson approximation and introduces exact hypothesis testing methods based on these properties.
Findings
Monotonicity properties of the Poisson approximation are proven.
Exact tests for binomial parameter p are developed.
Applications improve hypothesis testing accuracy.
Abstract
Certain monotonicity properties of the Poisson approximation to the binomial distribution are established. As a natural application of these results, exact (rather than approximate) tests of hypotheses on an unknown value of the parameter of the binomial distribution are presented.
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