Approximating the Lower Binomial Confidence Limit
- 1 December 1968
- journal article
- research article
- Published by JSTOR in Journal of the American Statistical Association
- Vol. 63 (324) , 1413
- https://doi.org/10.2307/2285894
Abstract
An earlier article [1] presented two formulas for approximating the upper binomial confidence limit from a sample of size n with c “defectives” drawn randomly from an infinite population with probability p of a defective. The present article presents two complementary formulas for approximating the lower binomial confidence limit p, based on m, the lower confidence limit for the paramater m of a Poisson distribution. These approximations are easy to calculate and have precisely specified bounds on their error over stated ranges of n and c/n. The error of the simpler formula is guaranteed to be within .1% of the exact binomial confidence limit when n ≥ 16 and c/n ≤ 1/8. The relative error of the second formula is not more than .1% when n ≥ 16 and . Values of m for small values of c are readily available from tables of the Poisson and chi-square distributions. For c ≥ 50, a simple formula permits approximating m with no more than .069% relative error. A procedure is given for approximating p when ,...Keywords
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