: L iving ▁people ▁Category : Univers ity ▁of ▁Science ▁and ▁Technology ▁of ▁China ▁al umn i ▁Category : B ran de is ▁University ▁al umn i ▁Category : Ch inese ▁diss idents ▁Category : Ch inese ▁blog gers ▁Category : Ch inese ▁document ary ▁film m akers ▁Category : Pe ople ' s ▁Republic ▁of ▁China ▁writers ▁Category : R oss ▁School ▁of ▁Business ▁al umn i <0x0A> </s> ▁The ▁general ised ▁hyper bol ic ▁distribution ▁( G H ) ▁is ▁a ▁continuous ▁probability ▁distribution ▁defined ▁as ▁the ▁normal ▁variance - mean ▁mixture ▁where ▁the ▁mixing ▁distribution ▁is ▁the ▁generalized ▁inverse ▁Gaussian ▁distribution ▁( G IG ). ▁Its ▁probability ▁density ▁function ▁( see ▁the ▁box ) ▁is ▁given ▁in ▁terms ▁of ▁modified ▁B essel ▁function ▁of ▁the ▁second ▁kind , ▁denoted ▁by ▁. ▁It ▁was ▁introduced ▁by ▁Ole ▁Bar nd or ff - N iel sen , ▁who ▁studied ▁it ▁in ▁the ▁context ▁of ▁physics ▁of ▁wind - b low n ▁sand . ▁ ▁Properties ▁ ▁Linear ▁transformation ▁ ▁This ▁class ▁is ▁closed ▁under ▁aff ine ▁transformations . ▁ ▁Sum m ation ▁ ▁Bar nd or ff - N iel sen ▁and ▁Hal green ▁proved ▁that ▁the ▁G IG ▁distribution ▁is ▁infinitely ▁divis ible ▁and ▁since ▁the ▁G H ▁distribution ▁can ▁be ▁obtained ▁as ▁a ▁normal ▁variance - mean ▁mixture ▁where ▁the ▁mixing ▁distribution ▁is ▁the ▁generalized ▁inverse ▁Gaussian ▁distribution , ▁Bar nd or ff - N iel sen ▁and ▁Hal green ▁showed ▁the ▁G H ▁distribution ▁is ▁infinitely ▁divis ible ▁as