Confidence Intervals for Some Functions of Several Bernoulli Parameters with Reliability Applications

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Abstract
The estimation of functions of Bernoulli parameters is of interest in reliability theory. In this article, the theory of exponential families is used to obtain exact confidence limits for products and quotients of Bernoulli parameters when negative binomial observations are available from each population. Sampling methods based on compound Poisson distribution are suggested for estimating more general functions such as sums of products of Bernoulli parameters. Finally, it is shown that exact confidence limits for products can be obtained by a discrete analog of the Lieberman-Ross procedure, which exploits the independence of the minimum and difference of geometric variates.

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