iid[k_] := TransformedDistribution[Abs[Sum[Exp[2 Pi I a[i]], {i, k}]],
Table[Distributed[a[i], UniformDistribution], {i, k}]]

Plot[PDF[iid[5],x],{x,0,5}]

iid[k_] := TransformedDistribution[Norm[Sum[{Cos[a[i]], Sin[a[i]]}, {i, k}]],
Table[Distributed[a[i], UniformDistribution], {i, k}]]