What is $E\left[\min\left(\frac{1}{X}\right)\right]=?$, where $X$ is a Rician distributed random variable.
I know from this article that the first moment of an inverse Rician distributed random variable is $E[Y] = \frac{\sqrt{\pi}}{\sqrt{2}\sigma}\exp\left(-\frac{s^2}{4\sigma^2}\right)I_0\left(\frac{s^2}{4\sigma^2}\right)$, where $Y=\frac{1}{X}$, $s$ is the noncentrality parameter of $X$, and $2\sigma^2$ is the variance of the noise.
With this information, I can bound $E\left[\min\left(\frac{1}{X}\right)\right] < E[Y]$. But I need something more specific.