Two dotted lines for reference distribution in QuantilePlot

Question

I'm using QuantilePlot to assess if my data fits a normal distribution using Mathematica 11.3.

My data set is large, 500000 points. A histogram of my data plotted with a normal distribution visually shows excellent agreement.

Here I use QuantilePlot to compare with a normal distribution (I get the same result if I explicitly use a normal distribution as the second data set):

QuantilePlot[data, ImageSize -> Large]

I can't find any reference to QuantilePlot plotting two parallel lines as the reference line. My data matches the lower of these two lines very well, but it is not clear what that means.

I tried plotting the quantiles of data against itself:

QuantilePlot[data, data, ImageSize->Large]

This should be a perfect match, and it is, but again with the lower dotted line.

To try this for yourself I came up with:

normaldist=RandomVariate[NormalDistribution[1,0.5],100000];
QuantilePlot[normaldist, normaldist, PlotRange->{{0,0.02},{-0.01,0.02}}, ImageSize->Large]

What is the second dotted line? All the examples in the documentation do not show a second line until you 'zoom in' using PlotRange.

Answer 1

At first glance this appears to be a bug. I suggest reporting it to WRI Support.

As a workaround you only need to remove the PlotRange option and the plot will display with the single reference line.

QuantilePlot[normaldist, normaldist, 
   ImageSize -> Large
   ReferenceLineStyle -> Directive[Orange, Thick]]

Hope this helps.

Answer 2

I ended up making a Quantile-Quantile plot myself to get around this. It's really slow and doesn't give the exact same result as QuantilePlot (less points?). But it will do. Perhaps someone else has a better way?

qsize = 0.00001;
quantiles = Quantile[data, #] & /@ Range[qsize, 1, qsize];
normalquantiles = 
  Quantile[NormalDistribution[Mean[data], 
      StandardDeviation[data]], #] & /@ Range[qsize, 1, qsize];
Show[ListPlot[Transpose[{normalquantiles, quantiles}], 
  PlotRange -> {{87.6, 89.65}, All}, ImageSize -> Large], 
 Plot[x, {x, 86, 92}, PlotStyle -> Directive[{Lighter, Dotted}]]]

Gives