Dear Claude,

Thank you very much for your help:)

Hi Jim,

For the following data, how can I determine the closest density curve (Regression or NeuralNet) to Observeddata's density curve?

Thank you

Observeddata = {5.3, 2.5, 5, 5.3, 5.8, 4, 3, 3, 3.3, 5.1, 2.7, 2, 3.5, 5.3, 5.6, 4.4, 4.6, 5.3, 4.4, 6.6, 6, 3.5, 4.8, 5.3, 5.3, 6.6, 6, 3.6, 2.7, 4.4, 5.3, 5.3, 6, 4.4, 7.1, 3.5};

Regression = {5.8, 2.2, 6, 5.5, 5.4, 4.3, 4, 3, 4, 5.5, 3, 2, 4, 5.5, 6, 4, 5, 5.3, 4.8, 6, 6.5, 4.5, 5, 5.4, 5.1, 6.2, 6.5, 3.7, 3.1, 4.7, 5, 4.8, 5.7, 4.4, 7, 3.2}

NeuralNet = {6, 3, 5.1, 6, 5, 4, 4.7, 3.3, 4.1, 5, 3.2, 2.3, 4.7, 5, 6.5, 4.1, 5.5, 5.9, 4.7, 7, 6.8, 4.7, 4.9, 5.3, 5.2, 6.7, 6.1, 3.2, 3.9, 4.2, 5.4, 4.2, 5.1, 4.1, 6.7, 3};

{xmin, xmax} = MinMax[Flatten[{Observeddata, Regression}]];

skd1 = SmoothKernelDistribution[Observeddata];

skd2 = SmoothKernelDistribution[Regression];

skd3 = SmoothKernelDistribution[NeuralNet];

Plot[{PDF[skd1, x], PDF[skd2, x], PDF[skd3, x]}, {x, xmin, xmax}];

Attachments:

If one has a large number of sample points as you do, you're almost always better off using a nonparametric density estimate for the two distributions. Such estimates allow for a much more interpretable figure that two overlaid histograms:

data1 = RandomVariate[NormalDistribution[0, 1], 500];
data2 = RandomVariate[NormalDistribution[3, 1/2], 500];
{xmin, xmax} = MinMax[Flatten[{data1, data2}]];
skd1 = SmoothKernelDistribution[data1];
skd2 = SmoothKernelDistribution[data2];
Plot[{PDF[skd1, x], PDF[skd2, x]}, {x, xmin, xmax}]

As far as an "overlap ratio", you'll need to define what you mean by that.

Histogram[{data1,data2}]

?