最尤推定値とCramér–von Mises推定値を比べる
最尤推定値を使い，Cramér–von Mises検定統計を最適化して，正規分布の母数推定値を視覚的に比べる．
data = BlockRandom[SeedRandom[2];
RandomVariate[NormalDistribution[], 100]];cvmFit[μ_ ? NumericQ, σ_ ? NumericQ, dist_] := CramerVonMisesTest[data, dist[μ, σ], "TestStatistic"];
cvmPar = Quiet[FindMinimum[cvmFit[μ, σ, NormalDistribution], {{μ}, {σ}}]];mlePar = FindDistributionParameters[data, NormalDistribution[μ, σ]];Show[Plot3D[cvmFit[μ, σ, NormalDistribution], {μ, -3, 3}, {σ, 0, 6}, ColorFunction -> ColorData["SouthwestColors"], PlotRange -> {{-2, 2}, {0, 3}, {-10, 35}}, MeshFunctions -> {#3&}, MeshStyle -> Gray, Mesh -> 30, BoxRatios -> 1], Graphics3D[{Darker@Blue, Thickness[.01], Line[{{μ, σ, 40}, {μ, σ, -20}} /. cvmPar[[2]]]}], Graphics3D[{Darker@Red, Thickness[.01], Line[{{μ, σ, 40}, {μ, σ, -20}} /. mlePar]}]]