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Given a gamma population with known shape parameter $\alpha$, we develop ageneral theory for estimating a function $g(\cdot)$ of the scale parameter$\beta$ with bounded variance. We begin by defining a sequential samplingprocedure with $g(\cdot)$ satisfying some desired condition in proposing thestopping rule, and show the procedure enjoys appealing asymptotic properties.After these general conditions, we substitute $g(\cdot)$ with specificfunctions including the gamma mean, the gamma variance, the gamma rateparameter, and a gamma survival probability as four possible illustrations. Foreach illustration, Monte Carlo simulations are carried out to justify theremarkable performance of our proposed sequential procedure. This is furthersubstantiated with a real data study on weights of newly born babies.

Estimating a function of the scale parameter in a gamma distribution with bounded variance