An Unusual Application of Cram´er-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 Cram´er-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.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 18, 2019, Art. #55

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Nitis Mukhopadhyay, Srawan Bishnoi, "An Unusual Application of Cram´er-Rao Inequality to Prove the Attainable Lower Bound for a Ratio of Complicated Gamma Functions," WSEAS Transactions on Mathematics, vol. 18, pp. 439-445, 2019, DOI:
Nitis Mukhopadhyay, Srawan Bishnoi. An Unusual Application of Cram´er-Rao Inequality to Prove the Attainable Lower Bound for a Ratio of Complicated Gamma Functions. WSEAS Transactions on Mathematics. 2019;18:439-445.
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