A Simple Expression for Mill's Ratio of the Student's $t$-Distribution

This work addresses a theoretical gap in probability theory for researchers in statistics and machine learning, but it is incremental as it builds directly on existing conjectures.

The paper tackles the problem of deriving a simple expression for Mill's ratio of the Student's t-distribution, and uses it to prove a conjecture from a prior multi-armed bandit analysis, providing a theoretical result without specific numerical gains.