Interval Estimation of Bounded Variable Means via Inverse Sampling ∗

It is a ubiquitous problem to estimate the means of bounded random variables. Specially, the problem of estimating the probability of an event can be formulated as the estimation of the mean of a Bernoulli variable. Moreover, in many applications, one needs to estimate a quantity μ which can be bounded in [0, 1] after proper operations of scaling and translation. A typical approach is to design an experiment that produces a random variable X distributed in [0, 1] with expectation μ, run the experiment independently a number of times, and use the average of the outcomes as the estimate [2]. The objective of this paper is to develop interval estimation methods for means of bounded variables based a sequential sampling scheme described as follows. Let X ∈ [0, 1] be a bounded random variable defined in a probability space (Ω,F ,Pr) with mean value E[X] = μ ∈ (0, 1). We wish to estimate the mean of X by using a sequence of i.i.d. random samples X1, X2, · · · of X based on the following inverse sampling scheme: Continue sampling until the sample size reach a number n such that the sample sum ∑