Gamma

dist=GammaDistribution[α,λ]

PDF[dist,z]

Manipulate[Plot[PDF[GammaDistribution[α,λ],x],{x,0,20},Filling->Axis],{α,1,6},{λ,2,6}]

Manipulate[Plot[Table[PDF[GammaDistribution[α,λ],x],{α,{1,4,6}}]//Evaluate,{x,0,20},Filling->Axis],{λ,2,6}]

Manipulate[Plot[Table[PDF[GammaDistribution[α,λ],x],{λ,{2,4,6}}]//Evaluate,{x,0,20},Filling->Axis],{α,1,6}]

Mean[dist]

Median[dist]

Variance[dist]

StandardDeviation[dist]

Skewness[dist]

Kurtosis[dist]

CharacteristicFunction[dist,t]

Random[GammaDistribution[1,1]]