version ▁ 2 ". ▁ ▁However ▁this ▁is ▁not ▁a ▁standard ▁nom en cl ature . ▁ ▁Version ▁ 1 ▁ ▁Kn own ▁also ▁as ▁the ▁exponential ▁power ▁distribution , ▁or ▁the ▁generalized ▁error ▁distribution , ▁this ▁is ▁a ▁paramet ric ▁family ▁of ▁symmetric ▁distributions . ▁ ▁It ▁includes ▁all ▁normal ▁and ▁Lap lace ▁distributions , ▁and ▁as ▁limit ing ▁cases ▁it ▁includes ▁all ▁continuous ▁uniform ▁distributions ▁on ▁bounded ▁intervals ▁of ▁the ▁real ▁line . ▁ ▁This ▁family ▁includes ▁the ▁normal ▁distribution ▁when ▁ ▁( with ▁mean ▁ ▁and ▁variance ▁) ▁and ▁it ▁includes ▁the ▁Lap lace ▁distribution ▁when ▁. ▁As ▁, ▁the ▁density ▁converges ▁point wise ▁to ▁a ▁uniform ▁density ▁on ▁. ▁ ▁This ▁family ▁allows ▁for ▁t ails ▁that ▁are ▁either ▁heav ier ▁than ▁normal ▁( when ▁) ▁or ▁l ighter ▁than ▁normal ▁( when ▁). ▁ ▁It ▁is ▁a ▁useful ▁way ▁to ▁paramet ri ze ▁a ▁continu um ▁of ▁symmetric , ▁pl aty k urt ic ▁dens ities ▁sp anning ▁from ▁the ▁normal ▁() ▁to ▁the ▁uniform ▁density ▁( ), ▁and ▁a ▁continu um ▁of ▁symmetric , ▁le pt ok urt ic ▁dens ities ▁sp anning ▁from ▁the ▁Lap lace ▁() ▁to ▁the ▁normal ▁density ▁( ). ▁ ▁Parameter ▁estimation ▁ ▁Parameter ▁estimation ▁via ▁maximum ▁lik elihood ▁and ▁the ▁method ▁of ▁moments ▁has ▁been ▁studied . ▁ ▁The ▁estimates ▁do ▁not ▁have ▁a ▁closed ▁form ▁and ▁must ▁be ▁obtained ▁numer ically . ▁ ▁Est im ators ▁that ▁do ▁not ▁require ▁numerical ▁calculation ▁have ▁also ▁been ▁proposed . ▁ ▁The ▁generalized