Abstract
Many a times a need may arise to estimate either a certain ratio or the sum of the shape parameters of two independent gamma populations. We try to tackle this problem through appropriate and novel two-stage sampling strategies. The first part of this paper deals with developing a two-stage methodology to estimate the ratio \(\alpha /(\alpha +\beta )\) coming from two independent gamma populations with parameters \((\alpha ,1)\) and \((\beta ,1)\) respectively. We assume a weighted squared error loss function and aim at controlling the associated risk function per unit cost by bounding it from above by a known constant \(\omega .\) We also establish first-order properties of our stopping rules. The second part of this paper deals with obtaining a two-stage sampling procedure to estimate the sum \(\alpha +\beta \) instead. We also provide extensive simulation analysis and real data analysis using data from cancer studies to show encouraging performances of our proposed stopping strategies.
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Bapat, S.R. A novel sequential approach to estimate functions of parameters of two gamma populations. Metrika 86, 627–641 (2023). https://doi.org/10.1007/s00184-022-00888-9
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DOI: https://doi.org/10.1007/s00184-022-00888-9