Stochastic orderings, folded beta distributions and fairness in coin flips

This paper studies stochastic orderings for folded beta distributions. A necessary and sufficient condition for one folded beta random variable to be larger than another in likelihood ratio order is obtained. The work is motivated by the recent results of Porzio and Ragozini on stochastic orderings for folded binomial distributions. Beta distributions are commonly used to model proportions or probabilities, particularly as conjugate distributions for binomial random variables. Stochastic orderings may arise, for instance, in considerations of fairness in coin flips.