Interesting, thanks for sharing.
Also interesting, a Google search on <probabilityscaleplot site:community.wolfram.com> gives only 3 different hits as of 2021-03-19, which could mean that not too many people use this function.
Related to your problem, I also cannot confirm that ProbabilityScalePlot[]
works or works well with WeightedData[]
as argument.
I completed a textbook problem on the theoretical and empirical distribution of the sum of five dice rolls including various plots, they all looked correct: I have completed and mastered the problem, as confirmed by the official solutions manual.
As a finishing touch I transformed/converted the given empirical table to weighted data (which is a legit technique and a very common thing to do in working with probability theory problems or statistics problems; I have much successful experience with this technique); but when I try to use this "data" as argument for the function, the graph shows wrong points, wrong slope, a graph which seemingly has nothing to do with my input.
I am not calling it a bug because of course there is some chance that I might be doing something wrong, like wrong syntax/wrong usage (user error). If I am wrong, then I don't mind, I have moved on yet.
Anyway, unless an identified Wolfram developer asks me to provide the full problem/solution/my work, I will leave it like that. I am busy with other things (even if it's "only" watching tennistv), it's not my job, I have other things to do than helping Wolfram correct their product (sorry for my poor attitude lol). Whoever reads this post take it as a warning: the ProbabilityScalePlot[WeightedData[]]
-idiom might not produce the desired output, or you should double check if the plot really does show the correct graph.
Personally, I don't care if that idiom produces the wrong output (and I believe that only very few people in the world have tried it). I really don't. I am posting this warning only to get the info out, so that others become aware. I took a note (my problem/solution is written in German) in my *.nb-file, so I am over it. But somebody at Wolfram should care. @Wolfram developers (the individual responsible for the statistics functions), you have all the info you need for investigation (sum of 5 dice rolls, generate pseudo-empirical distribution (~tally), convert to weighted data, use probabilityscaleplot and question what you're seeing as result!).
Ah with, here is some code snippet for the developer to study/investigate:
n = 2048;
lis1 = {0, 0, 4, 4, 29, 35, 41, 66, 122, 145, 165, 214, 216, 191, 205, 162, 144, 115, 89, 43, 31, 14, 6, 3, 3, 1, 0};
lis2 = Range[4.5, 31.5, 1];
Total[lis1] == n;(*True*)
d\[ScriptCapitalD] = DataDistribution["Histogram", {lis1*1/(n*1), lis2}, 1, n];
data = Transpose@{Range[5, 30], Most@lis1};
data2 = Transpose@{Range[7, 29], Take[lis1, {3, 25}]};
wdata = WeightedData[data[[All, 1]], data[[All, 2]]];
wdata2 = WeightedData[data2[[All, 1]], data2[[All, 2]]];
rvdata = RandomVariate[d\[ScriptCapitalD], 10^3];
ProbabilityScalePlot[{wdata, rvdata, wdata2}, PlotLegends -> {"wdata", "rvdata", "wdata2"}]
When you roll 5 dice, take their sum and examine the probability distribution of the sum, the rvdata graph shows the correct plot. The plot of wdata has to be a joke. No offense. Now let me continue to enjoy my tennis, bye :P