e . ▁the ▁product ▁of ▁ ▁exponential ▁power ▁distributions ▁with ▁the ▁same ▁ ▁and ▁ ▁parameters , ▁is ▁the ▁only ▁probability ▁density ▁that ▁can ▁be ▁written ▁in ▁the ▁form ▁ ▁and ▁has ▁independent ▁marg inals . ▁The ▁results ▁for ▁the ▁special ▁case ▁of ▁the ▁Mult ivari ate ▁normal ▁distribution ▁is ▁originally ▁attributed ▁to ▁Max well . ▁ ▁Version ▁ 2 ▁ ▁This ▁is ▁a ▁family ▁of ▁continuous ▁probability ▁distributions ▁in ▁which ▁the ▁shape ▁parameter ▁can ▁be ▁used ▁to ▁introduce ▁ske w . ▁ ▁When ▁the ▁shape ▁parameter ▁is ▁zero , ▁the ▁normal ▁distribution ▁results . ▁ ▁Pos itive ▁values ▁of ▁the ▁shape ▁parameter ▁yield ▁left - ske wed ▁distributions ▁bounded ▁to ▁the ▁right , ▁and ▁negative ▁values ▁of ▁the ▁shape ▁parameter ▁yield ▁right - ske wed ▁distributions ▁bounded ▁to ▁the ▁left . ▁Only ▁when ▁the ▁shape ▁parameter ▁is ▁zero ▁is ▁the ▁density ▁function ▁for ▁this ▁distribution ▁positive ▁over ▁the ▁whole ▁real ▁line : ▁in ▁this ▁case ▁the ▁distribution ▁is ▁a ▁normal ▁distribution , ▁otherwise ▁the ▁distributions ▁are ▁shift ed ▁and ▁possibly ▁revers ed ▁log - normal ▁distributions . ▁ ▁Parameter ▁estimation ▁ ▁Param eters ▁can ▁be ▁estimated ▁via ▁maximum ▁lik elihood ▁estimation ▁or ▁the ▁method ▁of ▁moments . ▁ ▁The ▁parameter ▁estimates ▁do ▁not ▁have ▁a ▁closed ▁form , ▁so ▁numerical ▁calculations ▁must ▁be ▁used ▁to ▁compute ▁the ▁estimates . ▁ ▁Since ▁the ▁sample ▁space ▁( the ▁set ▁of ▁real ▁numbers ▁where ▁the ▁density ▁is ▁non - zero ) ▁depends ▁on ▁the ▁true ▁value ▁of ▁the ▁parameter , ▁some ▁standard ▁results ▁about ▁the