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

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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.

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Acknowledgements

We are grateful to the Editor-in-Chief, the anonymous Associate Editor and two reviewers for their enthusiastic assessment.

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Authors and Affiliations

  1. Department of Statistics, University of Connecticut, Austin Building U-4120, 215 Glenbrook Rd, Storrs, CT, 06269-4120, USA

    Nitis Mukhopadhyay & Srawan Kumar Bishnoi

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  1. Nitis Mukhopadhyay
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  2. Srawan Kumar Bishnoi
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Correspondence to Nitis Mukhopadhyay.

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Mukhopadhyay, N., Bishnoi, S.K. An Unusual Application of Cramér-Rao Inequality to Prove the Attainable Lower Bound for a Ratio of Complicated Gamma Functions. Methodol Comput Appl Probab 23, 1507–1517 (2021). https://doi.org/10.1007/s11009-020-09822-w

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  • DOI: https://doi.org/10.1007/s11009-020-09822-w

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