Inthispaperweconsidersomerelatednegativehypergeometricdistributionsarisingfromtheproblemofsamplingwithoutreplacementfromanurncontainingballsofdifferentcoloursandindifferentproportionsbutstoppingonlyaftersomespecificnumberofballsofdifferentcolourshavebeenobtained.Withtheaidofsomesimplerecurrencerelationsandidentitiesweobtaininthecaseoftwocoloursthemomentsforthemaximumnegativehypergeometricdistribution,theminimumnegativehypergeometricdistribution,thelikelihoodrationegativehypergeometricdistributionandconsequentlythelikelihoodproportionalnegativehypergeometricdistributiuon.TotheextentthatthesamplingschemeisapplicabletomodellingdataasillustratedwithabiologicalexampleandinfactmanysituationsofestimatingBernoulliparametersforbinarytraitswithinafinitepopulation,theseareimportantfirst-stepresults.
