SmoothDensityHistogram[data, Automatic,"PDF",ColorFunction->
 "AvocadoColors",PlotRangePadding->None,PlotPoints->200]

n = 10000000;
r2 = 0.1;
choise = RandomChoice[{[Pi] r2, 1} -> {0, 1}, n];
box = RandomReal[1, {n, 2}];
circle = Transpose@{0.5 + # Cos@#2, 0.5 + # Sin@#2} &[
   Sqrt@RandomReal[r2, n], RandomReal[2 [Pi], n]];
pts = box choise + circle (1 - choise);

Grid[{{ListPlot[pts[[;; ;; 300]], AspectRatio -> Automatic,
    PlotLabel -> "Data"],
   SmoothDensityHistogram[pts[[;; ;; 300]], Automatic,
    PlotRange -> {{0, 1}, {0, 1}},
    PlotLabel -> "Bandwidth = Automatic"]},
  {SmoothDensityHistogram[pts[[;; ;; 300]], .1,
    PlotRange -> {{0, 1}, {0, 1}},
    PlotLabel -> "Bandwidth = 0.1"],
   SmoothDensityHistogram[pts[[;; ;; 300]], .02,
    PlotRange -> {{0, 1}, {0, 1}},
    PlotLabel -> "Bandwidth=0.02"]}}]