Slice Distributions from Data 

Compare the PDF from the process and simulation data at time .

In[1]:=

X proc = WienerProcess[1, 1]; data = RandomFunction[proc, {0, 10, 0.1}, 10^3];

In[2]:=

X Show[Plot[Evaluate[PDF[proc[5], x]], {x, -1, 11}, Filling -> Axis], SmoothHistogram[data["SliceData", 5], Filling -> Axis], PlotRange -> {{-1, 11}, All}]

Out[2]=

Compute several different slice distributions and overlay on simulation data.

In[3]:=

X plot1 = ListLinePlot[RandomFunction[proc, {0, 10, 0.1}, 25]]; plot2 = DistributionChart[Transpose@(data["SliceData", Range[10]]), ChartStyle -> Opacity[0.7]]; Show[plot1, plot2, PlotRange -> {{0, 11}, Automatic}]

Out[3]=