估计多变量非参数分布的概率和期望
使用 SmoothKernelDistribution 的二元密度估计的概率密度函数(PDF),表示了它的生成数据以及连续幕和的期待值.
dist = MixtureDistribution[{2, .1}, {MultinormalDistribution[-1 {1, 1}, 2 IdentityMatrix[2]], MultinormalDistribution[2 {.5, .5}, .01 IdentityMatrix[2]]}];
BlockRandom[SeedRandom[15];data = RandomVariate[dist, 250]];𝒟 = SmoothKernelDistribution[data];Show[Plot3D[PDF[𝒟, {x, y}], {x, -6, 5}, {y, -6, 5}, PlotRange -> {{-6, 5}, {-6, 5}, All}, ColorFunction -> (Opacity[Rescale[#3, {0, .6}, {0, 1}], ColorData["DeepSeaColors"][#3]]&), Mesh -> 45, MeshStyle -> Gray, MeshFunctions -> {#3&}, PlotPoints -> 50, ImageSize -> 550, ViewPoint -> {Pi, -Pi, 1}], ListPointPlot3D[Partition[Flatten[Transpose[{data, ConstantArray[0, Length[data]]}]], 3], PlotStyle -> Directive[PointSize -> .0075]], AspectRatio -> 1, Boxed -> False]