FDistribution

dist=FRatioDistribution[n,m]

PDF[dist,z]

CDP[dist,z]

Manipulate[Plot[PDF[FRatioDistribution[n,m],x],{x,0,2},PlotRange->{0,1},Filling->Axis,Exclusions->None],{m,1,20},{n,2,20}]

Manipulate[Plot[Table[PDF[FRatioDistribution[n,m],x],{n,{2,5,20}}]//Evaluate,{x,0,2},PlotRange->{0,1},Filling->Axis,Exclusions->None],{m,1,20}]

Manipulate[Plot[Table[PDF[FRatioDistribution[n,m],x],{m,{1,5,20}}]//Evaluate,{x,0,2},PlotRange->{0,1},Filling->Axis,Exclusions->None],{n,2,20}]

Mean[dist]

Median[dist]

Variance[dist]

StandardDeviation[dist]

Skewness[dist]

Kurtosis[dist]

CharacteristicFunction[dist,t]

Random[FRatioDistribution[1,1]]