Plot a sequence of histograms?

Question

How can I plot a sequence of histograms, one after the other, in 3D? Here is an example

Answer 1

When you have lots of data, you should consider using SmoothKernelDistribution or SmoothHistogram as I'm assuming that you must be thinking that the underlying true distribution is relatively smooth (and does not look like a jagged histogram).

These "nonparametric density estimates" work fine overlapped in 2D and if one really feels the need, one can create a 3D version much like what you've displayed for histograms.

(* Generate 4 sets of data *)
SeedRandom[12345];
data = RandomVariate[NormalDistribution[#[[1]], #[[2]]], 200] & /@ 
  {{0, 15}, {10, 12}, {20, 10}, {30, 5}};

(* Find smooth kernel density estimates *)
skd = SmoothKernelDistribution[#] & /@ data;

(* Plot resulting densities *)
ListPointPlot3D[Table[{10 (# - 1), x, PDF[skd[[#]], x]}, {x, -30, 50, .1}] & /@ {1, 2, 3, 4},
  Filling -> Bottom, BoxRatios -> {1, 1, 1}]

And the 2D version where the differences among curves is more readily apparent:

Plot[{PDF[skd[[1]], x], PDF[skd[[2]], x], PDF[skd[[3]], x], PDF[skd[[4]], x]},
  {x, -30, 50}, PlotLegends -> {"1", "2", "3", "4"}]

Answer 2

data1 = RandomVariate[NormalDistribution[0, 1], 500];
data2 = RandomVariate[NormalDistribution[1, 1/2], 500];
data3 = RandomVariate[NormalDistribution[2, 2], 500];

Histogram3D with a custom ChartElementFunction

cef[{{xmin_, xmax_}, {ymin_, ymax_}, {zmin_, zmax_}}, ___] := 
 Polygon[{{xmin, ymin, zmin}, {xmax, ymin, zmin}, {xmax, ymin, zmax}, {xmin, ymin, zmax}}]

Histogram3D[MapIndexed[Thread[{#, #2[[1]]}] &, {data1, data2, data3}], 
 {{-6, 6, 0.2}, {1}},
 ChartStyle -> {Red, Green, Blue},  BoxRatios -> 1, Axes -> True, 
 Boxed -> False, Method -> {"Canvas" -> None}, 
 FaceGrids -> {{-1, 0, 0}, {0, 1, 0}, {0, 0, -1}}, 
 ChartElementFunction -> cef]

Post-process Histogram output to 3D histograms:

ClearAll[rectanglesTo3DPolygons ]
rectanglesTo3DPolygons = Module[{i = 1}, 
    Cases[#, {dir__, rects : {{{_Rectangle}} ..}} :> 
      With[{j = i++}, {dir, Opacity[.7], 
        EdgeForm[{Thin, White}], {rects[[All, 1, 1]] /. 
          Rectangle[{a_, b_}, {c_, d_}, o___] :> 
           Polygon[{{a, j, b}, {c, j, b}, {c, j, d}, {a, j, d}}]}}], {0, Infinity}]] &;


hist = Histogram[{data1, data2, data3}, {.2},  
  ChartStyle -> {Red, Green, Blue}, ImageSize -> 300];

facegrids = {{{1, 0, 0}, {Range[3], {1}}}, {{-1, 0,  0}, {Range[3], {1}}},
  {{0, 0, 1}, {{}, Range[3]}}, {{0,  0, -1}, {{},Range[3]}}};

hist3d = Graphics3D[rectanglesTo3DPolygons@hist, 
   PlotRange -> {Automatic, {0, 4}, All}, BoxRatios -> 1, 
   FaceGrids -> facegrids, ImageSize -> 300];

Row[{hist, hist3d}]

hist2 = Histogram[{data1, data3}, {.2}, ChartStyle -> {Red,  Blue}, 
  ImageSize -> 300]; 
hist3d2 = Graphics3D[rectanglesTo3DPolygons@hist2, 
  PlotRange -> {Automatic, {0, 3}, All}, BoxRatios -> 1, 
  FaceGrids -> facegrids, ImageSize -> 300];

Row[{hist2, hist3d2}]

BarChart with a custom ChartElementFunction

heights = HistogramList[#, {-6, 6, .2}][[2]] & /@ {data1, data2, data3};

BarChart3D[heights, ChartLayout -> "Grid", 
 ChartStyle -> {{Red, Green, Blue}, None}, BarSpacing -> {0, 1}, 
 BoxRatios -> 1, Axes -> True, Boxed -> False, 
 Method -> {"Canvas" -> None}, 
 FaceGrids -> {{-1, 0, 0}, {0, 1, 0}, {0, 0, -1}}, 
 ChartElementFunction -> cef, PlotRangePadding -> {0, 2, 0}]