  >   0 ▁and ▁α 1   +   α 2   <   1 . ▁Here , ▁ ▁is ▁the ▁ 1 0 0 β % ▁quant ile ▁of ▁ ▁or ▁it ▁solves ▁for ▁ θ ▁in ▁equation ▁. ▁The ▁same ▁holds ▁for ▁an ▁a CD , ▁where ▁the ▁confidence ▁level ▁is ▁achieved ▁in ▁limit . ▁ ▁Point ▁estimation ▁▁ ▁Point ▁estim ators ▁can ▁also ▁be ▁constructed ▁given ▁a ▁confidence ▁distribution ▁estim ator ▁for ▁the ▁parameter ▁of ▁interest . ▁For ▁example , ▁given ▁H n ( θ ) ▁the ▁CD ▁for ▁a ▁parameter ▁ θ , ▁natural ▁choices ▁of ▁point ▁estim ators ▁include ▁the ▁median ▁M n   =   H n − 1 ( 1 / 2 ), ▁the ▁mean ▁, ▁and ▁the ▁maximum ▁point ▁of ▁the ▁CD ▁density ▁ ▁Under ▁some ▁mod est ▁conditions , ▁among ▁other ▁properties , ▁one ▁can ▁prove ▁that ▁these ▁point ▁estim ators ▁are ▁all ▁consistent . ▁ ▁Hyp oth esis ▁testing ▁▁ ▁One ▁can ▁derive ▁a ▁p - value ▁for ▁a ▁test , ▁either ▁one - s ided ▁or ▁two - s ided , ▁concerning ▁the ▁parameter   θ , ▁from ▁its ▁confidence ▁distribution ▁H n ( θ ). ▁Den ote ▁by ▁the ▁probability ▁mass ▁of ▁a ▁set ▁C ▁under ▁the ▁confidence ▁distribution ▁function ▁ ▁This ▁ps ( C ) ▁is ▁called ▁" support " ▁in ▁the ▁CD ▁inference ▁and ▁also ▁known ▁as ▁" bel ief " ▁in ▁the ▁fid u cial ▁literature . ▁We ▁have ▁ ▁( 1 ) ▁For ▁the ▁one -