Some new probability inequalities involving the ordered components of an $MTP_2$ random vector are derived, which provide an analytical proof of an important conjecture in the field of multiple hypothesis testing. This conjecture has been mostly validated so far using simulation.
"Some probability inequalities for ordered $\rm MTP\sb 2$ random variables: a proof of the Simes conjecture." Ann. Statist. 26 (2) 494 - 504, April 1998. https://doi.org/10.1214/aos/1028144846