AUTHORS: Nitis Mukhopadhyay, Srawan Bishnoi

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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 Cramer-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; Cramer-Rao inequality; Gamma functions; Point ´ estimation; Random CLT; Stopping time.

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