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

Nitis Mukhopadhyay () and Srawan Kumar Bishnoi ()
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Nitis Mukhopadhyay: University of Connecticut
Srawan Kumar Bishnoi: University of Connecticut

Methodology and Computing in Applied Probability, 2021, vol. 23, issue 4, 1507-1517

Abstract: 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.

Keywords: Asymptotic distribution; CLT; Confidence interval; Cramér-Rao inequality; Gamma functions; Point estimation; Random CLT; Stopping time; 60E15; 60F05; 60G40 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s11009-020-09822-w

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