A novel sequential approach to estimate functions of parameters of two gamma populations

Sudeep R. Bapat ()
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Sudeep R. Bapat: Indian Institute of Management

Metrika: International Journal for Theoretical and Applied Statistics, 2023, vol. 86, issue 6, No 2, 627-641

Abstract: 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 $$\alpha /(\alpha +\beta )$$ α / ( α + β ) coming from two independent gamma populations with parameters $$(\alpha ,1)$$ ( α , 1 ) and $$(\beta ,1)$$ ( β , 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 $$\omega .$$ ω . 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 $$\alpha +\beta $$ α + β 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.

Keywords: Cancer studies; Gamma distribution; Two-stage estimation; First-order asymptotic efficiency; 62L12; 62L05; 62F12; 62P30 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00184-022-00888-9

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