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

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  • Sudeep R. Bapat

    (Indian Institute of Management)

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.

Suggested Citation

  • Sudeep R. Bapat, 2023. "A novel sequential approach to estimate functions of parameters of two gamma populations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(6), pages 627-641, August.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:6:d:10.1007_s00184-022-00888-9
    DOI: 10.1007/s00184-022-00888-9
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    References listed on IDEAS

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    1. Sudeep R. Bapat, 2018. "On purely sequential estimation of an inverse Gaussian mean," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(8), pages 1005-1024, November.
    2. N. Mukhopadhyay & T. Solanky, 1997. "Estimation after sequential selection and ranking," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 45(1), pages 95-106, January.
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