Abstract:
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We propose a general procedure of estimating any positive parameter using such sequential fixed-accuracy confidence intervals. Estimation of positive parameters is essential in the areas of ecology, biology, medicine, nuclear power, study of cell membranes and others. For this methodology we have considered a consistent estimator of the parameter - it's maximum likelihood estimator. Beyond ecology, the procedure finds its applications in other affected by some disease, number of cells under genetic mutation, etc. Mukhopadhyay and Banerjee (2014b) developed a fixed-accuracy sequential confidence interval methodology for the mean of a negative binomial (NB) distribution with its thatch parameter unknown with applications in statistical ecology. In this paper, we develop a general structure for fixed-accuracy sequential confidence interval estimation methodology for any positive parameter of an arbitrary distribution which may be discrete or continuous. We construct our confidence interval, [T /d, dT] with d > 1, using a maximum likelihood (ML) estimator T. The methodology satisfies attractive properties such as asymptotic (as d ? 1+) consistency and asymptotic first-order efficiency
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