On Estimates of probabilities
L. N. Bol’shev · Theory of Probability and Its Applications · 1960
The problem of estimating an unknown probability in a series of independent trials is dealt -with. The experimental plan differs from the Bernoulli scheme. It is proved that the Clopper-Pearson method is applicable for the construction of interval estimates in an extensive class of :sequential type plans. The point and interval estimators for the Pólya scheme probability (negative binomial distribution) may serve as an example. An approximate formula for confidence limits is given. This is an asymptotic formula of percentage points of a B-distribution. The precision of this formula is greater than the corresponding normal and Poisson approximations.