LogNormal

dist = LogNormalDistribution[μ,σ]

PDF[dist,z]

CDF[dist,z]

Manipulate[Plot[PDF[LogNormalDistribution[μ,σ],x],{x,0,4},Filling->Axis,PlotRange->{0,0.4}],{μ,-1,3},{σ,0.5,1.5}]

Manipulate[Plot[Table[PDF[LogNormalDistribution[μ,σ],x],{μ,{-1,2,3}}]//Evaluate,{x,0,4},Filling->Axis,PlotRange->{0,0.4}],{σ,0.5,1.5}]

Manipulate[Plot[Table[PDF[LogNormalDistribution[μ,σ],x],{σ,{0.5,0.75,1.5}}]//Evaluate,{x,0,4},Filling->Axis],{μ,-1,3}]

Mean[dist]

Median[dist]

Variance[dist]

StandardDeviation[dist]

Skewness[dist]

Kurtosis[dist]

CharacteristicFunction[dist,t]

Random[LogNormalDistribution[0,1]]