Abstract
Point and interval probability estimates for an event that has never been observed in a Bernoulli trial series (0-event) are proposed and validated. In this case, the classical statistical methods yield a zero point estimate, which is often unacceptable in practice. Nonzero point and interval probability estimates for a 0-event are proposed and validated. A classication of samples by size for the case of a 0-event is proposed.
Highlights
Problem formulationEstimation of a nonrandom but unknown probability p of a certain random event X occurring in a single test is considered
L(p, x) = L(p | m, n) = pm(1−p)n−m is the likelihood function for the binomial statistical model, where x = (x1, . . . , xn) is the sample obtained as a result of performing n elementary independent experiments of observing the event X (xi ∈ {0, 1}, i = 1, n ), where 1 occurs in x m times and 0 occurs n − m times; Θ = [0, 1] is the closure of the set Θ
By the 0-event we mean the random event X that has never been observed in a series of Bernoulli trials
Summary
Estimation of a nonrandom but unknown probability p of a certain random event X occurring in a single test is considered. By the 0-event we mean the random event X that has never been observed in a series of Bernoulli trials (rather than the fact of obtaining a zero sample as in [10]). Formula (1) yields a zero point estimator of the probability of observing X, and formula (2) yields a zero estimated value of its variance. This estimate p = 0 is often unacceptable in practice. In this paper, which is a further development of [9], a nonzero point estimator of a 0-event is proposed and validated
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