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I saw the following representation in a paper that I was reading. Can anyone can shed any light on how it was developed?

this is the Paper - page 34

Radial representation of Probability Density Functions

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  • $\begingroup$ It looks like slices of 1-d kernel density estimates that are then aligned in a set of polar coordinates. Alot of statistical packages can do the individual parts, but I imagine it would be tedious to make a graphic so refined. If I were doing it myself I would probably make the vector geometries myself and then export it to a 3d graphics program, like ESRI's ArcScene. You should IMO link to the paper. $\endgroup$ – Andy W Apr 29 '14 at 12:38
  • $\begingroup$ @AndyW I linked to the paper $\endgroup$ – dassouki Apr 29 '14 at 12:40
  • $\begingroup$ Thank you. I would also note it appears in the graphic they estimate take slices by time of day, but that isn't strictly necessary (although convenient). You could estimate a KDE for all observations (e.g. smooth in the radius "travel time" dimension and the angle "time of day" dimension). Although I'm unaware what type of kernel one should use in such a situation. $\endgroup$ – Andy W Apr 29 '14 at 12:44
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    $\begingroup$ A 2d plot where you color each line according to the time of day is much simpler and easily accomplished in several statistical packages. I've used cyclical color ramps for similar plots in the past. The 3d is quite pretty and stunning though in this example as it is quite smooth. $\endgroup$ – Andy W Apr 29 '14 at 12:46
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    $\begingroup$ An interesting aspect of this plot--a similar issue was overlooked in at least one early textbook on circular statistics--is that the radial portrayal visually exaggerates the probabilities in the outer extremes, in direct proportion to their distance from the center of the plot. When this is coupled with the (huge) loss of perceptual accuracy in reading values in any pseudo-3D graphic, one is left admiring the pretty computer construct but wondering about it actual utility (and shaking one's head about its implicitly large Lie Factor). $\endgroup$ – whuber Apr 29 '14 at 17:00
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Don't do it! (unless it's for an art project)

Circular views are harder to interpret (e.g., harder to compare values and slopes). Straight lines turn into curves and curves turn into straight lines. Adding 3-D can only make it worse with additional obscuring and perspective distortion.

The paper Graphical Tests for Power Comparison of Competing Designs by Heike Hofmann et al. provides some experimental support for the above statement. One of their test cases shows that circular charts underperform even when the data is naturally circular (wind direction in their case, time of day in the question's example).

Something in between the two images below from the same paper should be easier to read and compare values across time. That is, I'd like to see the information from the first (7+ summary values per time interval) encoded more like the second (with lines and shaded areas).

enter image description here

enter image description here

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