Hi Amin,

I believe that the problem is where you position the PlotLegends. It would need to go into the Plot function. This can be achieved like so:

Show[Histogram[cana, Automatic, "PDF"], 
 Plot[Evaluate[
PDF[#, x] & /@ Evaluate[Normal[(Normal@FindDistribution[cana, 5, All, TargetFunctions -> "Continuous"])][[All, 1]]]], {x, 0, 1200}, PlotLegends -> Automatic]]

But as you can see the labels are just from 1 to 5. This might be better for you:

dists = Evaluate[Normal[(Normal@FindDistribution[cana, 5, All, TargetFunctions -> "Continuous"])][[All, 1]]]; Show[
Histogram[cana, Automatic, "PDF"], Plot[Evaluate[PDF[#, x] & /@ dists], {x, 0, 1200}, 
PlotLegends -> Evaluate[StringReplace[#, "Distribution" -> " Distribution"] & /@ ToString /@ (Head /@ dists)]]]

Here I first generate the estimates for the distributions. When I plot it, I use these distributions twice: first for the actual plotting and second for the labelling. The funny code in the Labelling bit is only to get a space before "Distribution".

If you require the entire distributions (not just the head label) then it is one (or two depending on how you count) function shorter:

dists = Evaluate[Normal[(Normal@FindDistribution[cana, 5, All, TargetFunctions -> "Continuous"])][[All, 1]]]; 
Show[Histogram[cana, Automatic, "PDF"], Plot[Evaluate[PDF[#, x] & /@ dists], {x, 0, 1200}, 
PlotLegends -> Evaluate[StringReplace[#, "Distribution" -> " Distribution"] & /@ ToString /@ dists]]]

Best wishes,

Marco

Dear Marco, Thank you so much for your help and elegantly instructive response. I will be more careful using the word " bug" .Should I edit the title ? Cheers, Amin.

Hi Amin,

I don't think that that is a bug. FindDistribution involves a stochastic process. If you fix the random seed the results will be exactly identical.

FindDistribution[cana, 5, All, TargetFunctions -> "Continuous", "RandomSeed" -> 23544325]

In other words,

FindDistribution[cana, 5, All, TargetFunctions -> "Continuous"]

changes every time you execute it, whereas

FindDistribution[cana, 5, All, TargetFunctions -> "Continuous", "RandomSeed" -> 23544325]

Does not.

BTW, you can also look at the difference of the estimated distributions without fixing the random seed. Here are all 5 estimates:

Show[Histogram[cana, Automatic, "PDF"], 
Plot[PDF[#, x], {x, 0, 1200}] & /@ Evaluate[Normal[(Normal@FindDistribution[cana, 5, All, TargetFunctions -> "Continuous"])][[All, 1]]]]

If you look for the different estimates of, say, the GammaDistribution if you run the thing several times it looks like this:

Show[Histogram[cana, Automatic, "PDF"], 
Plot[PDF[#, x], {x, 0, 1200}] & /@ 
Flatten[Table[Select[Normal[Normal[FindDistribution[cana, 5, All, 
TargetFunctions -> "Continuous"][[All, 1]]]][[All, 1]], Head[#] == GammaDistribution &], {5}]]]

I would assume that the variation between the estimates becomes smaller if you have more points in your dataset.

Cheers,

Marco

PS: I think one should only use the word "bug" in the title if it is confirmed.