Gamma variate generators with increased shape parameter range

devdoped gamma ge~erator:s are compact., nasty program~, and ~emss a saifnrm stoned over the operathg range, t~t are oab ~ vNtd for a > 1. A tran~ormation of variable together with a technique suggested by" Kinder.man and Monakan of generating random ,eariates u~ing the ratio of mniform variates are cnmbiaed to produce a fatuity of generators raid far all a > l/n where n is an arbitrary integer. Thus if s ks greater than uNty, variates with a tess than unity can be sam#ed. The cases n = 2 and n = 4 are considered explicitly aeM are shown to retain the feaVares of compactness, ease ~f and u~fform sDeed. Since the publication of the review paper of A~ki.nson and Pearce {2], there have appeared a large number of gamma variate generators covering the case ~ > I where ~ is the shape parameter. One of the more noteworthy methods is based on the generat technique of generating random varia~es using the ratio of uniform variates proposed originally by Kindermaa and Monahan {6]. Kinderman and Mona.ban [7] and Cheng and Feast [5] ;have suggested Mgorithms using this technique to generate gamma variates, The ~brme~ paper also comains some sound criteria for the choice of an optima1 alg{~ Pem~i<'m h'~ copy wtho~t~ fee a]~p~i~ gra~te~ p~x~vided that ~.he c, epies are not made or d~tr/ba~e~ &~ dh'e¢~ ~NU~ UK~ Cornm~m~c~mB~s hd) igN) ~*e ACM Nu.r~*be~' 7