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An Unusual Application of Cramér-Rao Inequality to Prove the Attainable Lower Bound for a Ratio of Complicated Gamma Functions

Author

Listed:
  • Nitis Mukhopadhyay

    (University of Connecticut)

  • Srawan Kumar Bishnoi

    (University of Connecticut)

Abstract

A specific function f(r) involving a ratio of complicated gamma functions depending upon a real variable r(> 0) is handled. Details are explained regarding how this function f(r) appeared naturally for our investigation with regard to its behavior when r belongs to R+. We determine explicitly where this function attains its unique minimum. In doing so, quite unexpectedly the customary Cramér-Rao inequality comes into play in order to nail down a valid proof of the required lower bound for f(r) and locating where is that lower bound exactly attained.

Suggested Citation

  • Nitis Mukhopadhyay & Srawan Kumar Bishnoi, 2021. "An Unusual Application of Cramér-Rao Inequality to Prove the Attainable Lower Bound for a Ratio of Complicated Gamma Functions," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1507-1517, December.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:4:d:10.1007_s11009-020-09822-w
    DOI: 10.1007/s11009-020-09822-w
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    References listed on IDEAS

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    1. Allan Gut & Nitis Mukhopadhyay, 2010. "On Asymptotic and Strict Monotonicity of a Sharper Lower Bound for Student’s t Percentiles," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 647-657, December.
    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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