Core Algorithms

Bivariate Continuous Distribution Functions

Compute and visualize multivariate continuous distribution functions.

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Clear[DistributionPlot3D];

DistributionPlot3D[dist_, {xmin_, xmax_}, {ymin_, ymax_}] :=

Module[{x, y, pdf, cdf, sf, hf},

{pdf, cdf, sf, hf} =

{Plot3D[PDF[dist, {x, y}], {x, xmin, xmax}, {y, ymin, ymax},

PlotRange -> {0, Automatic}, PlotLabel -> "PDF",

PlotStyle -> Lighter[ColorData[1, 1], .4], Filling -> Axis,

FillingStyle -> Lighter[ColorData[1, 1], 0.4],

MeshStyle -> GrayLevel[.8], MeshFunctions -> {#3 &},

Lighting -> "Neutral"],

Plot3D[CDF[dist, {x, y}], {x, xmin, xmax}, {y, ymin, ymax},

PlotRange -> {0, 1}, PlotLabel -> "CDF",

PlotStyle -> Lighter[ColorData[1, 2], 0.4], Filling -> Axis,

FillingStyle -> Lighter[ColorData[1, 2], 0.4],

MeshStyle -> GrayLevel[.8], MeshFunctions -> {#3 &},

Lighting -> "Neutral"],

Plot3D[

SurvivalFunction[dist, {x, y}], {x, xmin, xmax}, {y, ymin,

ymax}, PlotRange -> {0, 1}, PlotLabel -> "SF",

PlotStyle -> Lighter[ColorData[1, 3], .2], Filling -> Axis,

FillingStyle -> Lighter[ColorData[1, 3], .2],

MeshStyle -> GrayLevel[1], MeshFunctions -> {#3 &},

Lighting -> "Neutral"],

Plot3D[

HazardFunction[dist, {x, y}], {x, xmin, xmax}, {y, ymin, ymax},

PlotRange -> {0, Automatic}, PlotLabel -> "HF",

PlotStyle -> Lighter[ColorData[1, 4], 0.4], Filling -> Axis,

FillingStyle -> Lighter[ColorData[1, 4], 0.4],

MeshStyle -> GrayLevel[1], MeshFunctions -> {#3 &},

Lighting -> "Neutral"]};

GraphicsGrid[{{pdf, cdf}, {sf, hf}}, ImageSize -> 500]

];

DistributionPlot3D[BinormalDistribution[1/2], {-3, 3}, {-3, 3}]

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