▁be ▁a ▁distribution ▁on ▁the ▁parameter ▁space . ▁The ▁second ▁requirement ▁( R 2 ) ▁sets ▁a ▁restriction ▁on ▁the ▁function ▁so ▁that ▁infer ences ▁( point ▁estim ators , ▁confidence ▁intervals ▁and ▁hypothesis ▁testing , ▁etc .) ▁based ▁on ▁the ▁confidence ▁distribution ▁have ▁desired ▁frequent ist ▁properties . ▁This ▁is ▁similar ▁to ▁the ▁restrictions ▁in ▁point ▁estimation ▁to ▁ensure ▁certain ▁desired ▁properties , ▁such ▁as ▁un bi ased ness , ▁consist ency , ▁efficiency , ▁etc . ▁ ▁A ▁confidence ▁distribution ▁derived ▁by ▁in ver ting ▁the ▁upper ▁limits ▁of ▁confidence ▁intervals ▁( class ical ▁definition ) ▁also ▁satisfies ▁the ▁requirements ▁in ▁the ▁above ▁definition ▁and ▁this ▁version ▁of ▁the ▁definition ▁is ▁consistent ▁with ▁the ▁classical ▁definition . ▁ ▁Un like ▁the ▁classical ▁fid u cial ▁inference , ▁more ▁than ▁one ▁confidence ▁distributions ▁may ▁be ▁available ▁to ▁estimate ▁a ▁parameter ▁under ▁any ▁specific ▁setting . ▁Also , ▁unlike ▁the ▁classical ▁fid u cial ▁inference , ▁optim ality ▁is ▁not ▁a ▁part ▁of ▁requirement . ▁ ▁Depending ▁on ▁the ▁setting ▁and ▁the ▁criter ion ▁used , ▁sometimes ▁there ▁is ▁a ▁unique ▁" best " ▁( in ▁terms ▁of ▁optim ality ) ▁confidence ▁distribution . ▁But ▁sometimes ▁there ▁is ▁no ▁optimal ▁confidence ▁distribution ▁available ▁or , ▁in ▁some ▁extreme ▁cases , ▁we ▁may ▁not ▁even ▁be ▁able ▁to ▁find ▁a ▁meaning ful ▁confidence ▁distribution . ▁This ▁is ▁not ▁different ▁from ▁the ▁practice ▁of ▁point ▁estimation . ▁ ▁Ex amples ▁ ▁Example ▁ 1 : ▁Normal ▁mean ▁and ▁variance ▁▁ ▁Suppose ▁a ▁normal ▁sample ▁X