WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 18, 2019
An Unusual Application of Cram´er-Rao Inequality to Prove the Attainable Lower Bound for a Ratio of Complicated Gamma Functions
Authors: ,
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.