Role of Z-axis in SmoothHistogram3D?

Questions
,
1

Hi, I have plotted the following:

data1 = RandomVariate[
NormalDistribution[0.0014, 1.936 E - 005], {10000, 2}];

data2 = RandomVariate[
NormalDistribution[0.0013, 1.925 E - 005], {10000, 2}];

Manipulate[
SmoothHistogram3D[{data1, data2}, PlotStyle -> Opacity[opacity], 
PlotLegends -> {"Bi-section", "Genetic Algorithm"}], {{opacity, 1}, 
0.5, 1, 0.05, Appearance -> "Labeled"}]

I am a bit confused with the generated graph. I understand that the x and y axes are the “mean” of the normal distribution, however, I am not really sure what the z-axis is representing?
Also, Is there any possibility to specify the axis and what they should represent? If yes, please let me know how to do it.
Finally, Is there any possibility to change the plot colors? other than the automatic Blue and Orange that is generated?

Thanks!

2

What is 1.936 E - 005? Surprisingly, even Interpreter cannot decypher it:

Interpreter["Number"]["1.936 E-005"]

Assuming that it means 1.936*10^(-005), here is your plot:

data1 = RandomVariate[
   NormalDistribution[0.0014, 1.936*10^(-005)], {10000, 2}];
data2 = RandomVariate[
   NormalDistribution[0.0013, 1.936*10^(-005)], {10000, 2}];
Manipulate[
 SmoothHistogram3D[{data1, data2}, PlotStyle -> Opacity[opacity], 
  PlotLegends -> {"Bi-section", "Genetic Algorithm"}], {{opacity, 1}, 
  0.5, 1, 0.05, Appearance -> "Labeled"}]

The z values should be the probability density function (PDF) of the distributions.

3

Thanks!
Is there any possibility to change the plot colors? other than the automatic Blue and Orange that is generated?

4

Hi Mary,

To change the colors

PlotStyle -> {Directive[Opacity[opacity], Red], Directive[Opacity[opacity], Green]}