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Approximations to well known discrete distribution functions are the subject of a large number of publications, but little has been done to provide guidelines for the choice of an approximation which is as accurate as possible, but simple enough for hand calculation.The present study tries to fill this gap, by a report on the asymptotic and numerical properties of the previously published approximations, and of some new ones.Many thanks are due to Professo~s HEMELRIJK and VAN ZWET, for encouragement and criticism during the past two years.I am also grateful to Mr. YEH.MEYER .(forassistance in calculations and proofreading), Mrs. and Mr. HILLEBRAND (for typing and preparing illustrations), Mr. ZWARST and Mr. SUIKER (for reproduction
Helms et al. (Mon,) studied this question.