Weibull

dist = WeibullDistribution[α,β]

PDF[dist,z]

CDF[dist,z]

Manipulate[Plot[PDF[WeibullDistribution[α,β],x],{x,0,5},Filling->Axis],{α,0.5,4},{β,1,4}]

Manipulate[Plot[Table[PDF[WeibullDistribution[α,β],x],{α,{0.5,2,4}}]//Evaluate,{x,0,5},Filling->Axis],{β,1,4}]

Manipulate[Plot[Table[PDF[WeibullDistribution[α,β],x],{β,{1,2,4}}]//Evaluate,{x,0,5},Filling->Axis],{α,0.5,4}]

Mean[dist]

Median[dist]

Variance[dist]

StandardDeviation[dist]

Skewness[dist]

Kurtosis[dist]

CharacteristicFunction[dist,t]

Random[WeibullDistribution[1,1]]