A pr 2 00 9 Multistage Estimation of Bounded - Variable Means ∗

Multistage Estimation of Bounded - Variable Means ∗

In this paper, we develop a multistage approach for estimating the mean of a bounded variable. We first focus on the multistage estimation of a binomial parameter and then generalize the estimation methods to the case of general bounded random variables. A fundamental connection between a binomial parameter and the mean of a bounded variable is established. Our multistage estimation methods rig...

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...

Confidence Interval for the Mean of a Bounded Random Variable and Its Applications in Point Estimation

In this article, we derive an explicit formula for computing confidence interval for the mean of a bounded random variable. Moreover, we have developed multistage point estimation methods for estimating the mean value with prescribed precision and confidence level based on the proposed confidence interval.

A Link between Binomial Parameters and Means of Bounded Random Variables ∗

In this paper, we establish a fundamental connection between binomial parameters and means of bounded random variables. Such connection finds applications in statistical inference of means of bounded variables. 1 A Fundamental Identity Statistical inference of means of bounded random variables is frequently encountered in many areas of sciences and engineering. Since there exist rich techniques...

ar X iv : 0 70 4 . 01 15 v 2 [ m at h . G T ] 9 A pr 2 00 7 Smooth maps with singularities of bounded K - codimensions ∗ † Yoshifumi ANDO