  We build a valid p-value based on a concentration inequality for bounded
random variables introduced by Pelekis, Ramon and Wang. The motivation behind
this work is the calibration of predictive algorithms in a distribution-free
setting. The super-uniform p-value is tighter than Hoeffding and Bentkus
alternatives in certain regions. Even though we are motivated by a calibration
setting in a machine learning context, the ideas presented in this work are
also relevant in classical statistical inference. Furthermore, we compare the
power of a collection of valid p- values for bounded losses, which are
presented in previous literature.
