▁performance ▁of ▁parameter ▁estimates ▁will ▁not ▁automatically ▁apply ▁when ▁working ▁with ▁this ▁family . ▁ ▁App lications ▁ ▁This ▁family ▁of ▁distributions ▁can ▁be ▁used ▁to ▁model ▁values ▁that ▁may ▁be ▁normally ▁distributed , ▁or ▁that ▁may ▁be ▁either ▁right - ske wed ▁or ▁left - ske wed ▁relative ▁to ▁the ▁normal ▁distribution . ▁ ▁The ▁ske w ▁normal ▁distribution ▁is ▁another ▁distribution ▁that ▁is ▁useful ▁for ▁model ing ▁devi ations ▁from ▁normal ity ▁due ▁to ▁ske w . ▁ ▁Other ▁distributions ▁used ▁to ▁model ▁ske wed ▁data ▁include ▁the ▁g amma , ▁log normal , ▁and ▁We ib ull ▁distributions , ▁but ▁these ▁do ▁not ▁include ▁the ▁normal ▁distributions ▁as ▁special ▁cases . ▁ ▁Other ▁distributions ▁related ▁to ▁the ▁normal ▁ ▁The ▁two ▁generalized ▁normal ▁families ▁described ▁here , ▁like ▁the ▁ske w ▁normal ▁family , ▁are ▁paramet ric ▁families ▁that ▁extends ▁the ▁normal ▁distribution ▁by ▁adding ▁a ▁shape ▁parameter . ▁ ▁Due ▁to ▁the ▁central ▁role ▁of ▁the ▁normal ▁distribution ▁in ▁probability ▁and ▁statistics , ▁many ▁distributions ▁can ▁be ▁character ized ▁in ▁terms ▁of ▁their ▁relationship ▁to ▁the ▁normal ▁distribution . ▁ ▁For ▁example , ▁the ▁log - normal , ▁fol ded ▁normal , ▁and ▁inverse ▁normal ▁distributions ▁are ▁defined ▁as ▁transformations ▁of ▁a ▁normally - dist ributed ▁value , ▁but ▁unlike ▁the ▁generalized ▁normal ▁and ▁ske w - normal ▁families , ▁these ▁do ▁not ▁include ▁the ▁normal ▁distributions ▁as ▁special ▁cases . ▁Actually ▁all ▁distributions ▁with ▁finite ▁variance ▁are ▁in ▁the ▁limit ▁highly ▁related ▁to ▁the ▁normal ▁distribution . ▁The