h[x_]:=Piecewise[{{1,x<1},{Exp[-x],x≥1}}]

𝒟=ProbabilityDistribution[{"HF", h[x]},{x,0,∞}]

GraphicsGrid[Partition[Table[Plot[fun[𝒟,x],{x,0,4},Filling->Axis,PlotLabel->fun,ImageSize->200],{fun,{PDF,CDF,HazardFunction,SurvivalFunction}}],2,2]]

data=RandomVariate[𝒟,10^5];
Histogram[data,{0,6,.1},"PDF",ImageSize->300]