χ ▁is ▁the ▁sample ▁space ▁corresponding ▁to ▁data ▁X n ={ X 1 , ▁... , ▁X n }: ▁▁ ▁A ▁function ▁H n ( • ) ▁= ▁H n ( X n ,   • ) ▁on ▁ χ   ×   Θ   →   [ 0 ,   1 ] ▁is ▁called ▁a ▁confidence ▁distribution ▁( CD ) ▁for ▁a ▁parameter ▁ θ , ▁if ▁it ▁follows ▁two ▁requirements : ▁( R 1 ) ▁For ▁each ▁given ▁X n ▁ ∈ ▁ χ , ▁H n ( • ) ▁= ▁H n ( X n ,   • ) ▁ ▁is ▁a ▁continuous ▁cum ulative ▁distribution ▁function ▁on ▁ Θ ; ▁( R 2 ) ▁At ▁the ▁true ▁parameter ▁value ▁ θ   =   θ 0 , ▁H n ( θ 0 )   ≡   H n ( X n , ▁ θ 0 ), ▁as ▁a ▁function ▁of ▁the ▁sample ▁X n , ▁follows ▁the ▁uniform ▁distribution ▁U [ 0 ,   1 ]. ▁Also , ▁the ▁function ▁H ▁is ▁an ▁asympt otic ▁CD ▁( a CD ), ▁if ▁the ▁U [ 0 ,   1 ] ▁requirement ▁is ▁true ▁only ▁asympt ot ically ▁and ▁the ▁continu ity ▁requirement ▁on ▁H n ( • ) ▁is ▁dropped . ▁ ▁In ▁non techn ical ▁terms , ▁a ▁confidence ▁distribution ▁is ▁a ▁function ▁of ▁both ▁the ▁parameter ▁and ▁the ▁random ▁sample , ▁with ▁two ▁requirements . ▁The ▁first ▁requirement ▁( R 1 ) ▁simply ▁requires ▁that ▁a ▁CD ▁should