▁even ▁be ▁trac ed ▁back ▁to ▁Bay es ▁( 1 7 6 3 ) ▁and ▁Fish er ▁( 1 9 3 0 ). ▁Some ▁research ers ▁view ▁the ▁confidence ▁distribution ▁as ▁" the ▁Ne yman ian ▁interpretation ▁of ▁Fish er ' s ▁fid u cial ▁distributions ", ▁which ▁was ▁" fur iously ▁disput ed ▁by ▁Fish er ". ▁It ▁is ▁also ▁believed ▁that ▁these ▁" un product ive ▁disput es " ▁and ▁Fish er ' s ▁" st ub born ▁ins istence " ▁might ▁be ▁the ▁reason ▁that ▁the ▁concept ▁of ▁confidence ▁distribution ▁has ▁been ▁long ▁mis const ru ed ▁as ▁a ▁fid u cial ▁concept ▁and ▁not ▁been ▁fully ▁developed ▁under ▁the ▁frequent ist ▁framework . ▁Indeed , ▁the ▁confidence ▁distribution ▁is ▁a ▁purely ▁frequent ist ▁concept ▁with ▁a ▁purely ▁frequent ist ▁interpretation , ▁and ▁it ▁also ▁has ▁t ies ▁to ▁Bay esian ▁inference ▁concepts ▁and ▁the ▁fid u cial ▁arguments . ▁ ▁Definition ▁ ▁Class ical ▁definition ▁▁ ▁Class ically , ▁a ▁confidence ▁distribution ▁is ▁defined ▁by ▁in ver ting ▁the ▁upper ▁limits ▁of ▁a ▁series ▁of ▁lower - s ided ▁confidence ▁intervals . ▁In ▁particular , ▁▁ ▁For ▁every ▁α ▁in ▁( 0 ,   1 ), ▁let ▁( − ∞ ,   ξ n ( α )] ▁be ▁a ▁ 1 0 0 α % ▁lower - side ▁confidence ▁interval ▁for ▁ θ , ▁where ▁ ξ n ( α ) ▁=   ξ n ( X n , α ) ▁is ▁continuous ▁and ▁increasing ▁in ▁α ▁for ▁each