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Imagine there is a spherical volume filled with black spheres of different sizes. In projection, there are some painted blue regions which are intersected by those spheres. The blue errorbars come from the probability distribution of the spheres intersecting blue regions (in projection) while black errorbars come from the probability distribution of the spheres intersecting random beams. The following plot shows the two normalized and discrete probability density functions. How to show whether the blue PDF is taken from the black PDF using K-S method or any other method?

enter image description here

Rebel
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  • Aren't K-S in general and ks_2samp() in particular assume continuous distributions? – Severin Pappadeux Feb 16 '20 at 02:48
  • Yes, they do. In some cases though one can conservatively use them for discrete distributions. Given that I cannot repeat these measurements in order to create permutations, I am wondering if this is doable or else I should come up with something else. – Rebel Feb 16 '20 at 03:02
  • As first try, it looks like geometric distribution to me, so I would try to fit exponential (continuous analog of geometric), and then use K-S as samples against cont.distribution. – Severin Pappadeux Feb 16 '20 at 03:10
  • For black errorbars, geometric distribution could be assumed but I am sure that for blue errorbars that cannot be assumed since the probability of success, p, is not the same for every trial. – Rebel Feb 16 '20 at 04:22
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    Well, you don't have to assume anything for blue dots-bars. You are just asking if blue could come as realization of black distribution. – Severin Pappadeux Feb 16 '20 at 15:29
  • Does the fact that x-axis is in logarithmic scale matter as far as K-S method is concerned? – Rebel Feb 16 '20 at 17:43
  • No, it doesn't matter (well, it matters when you have to fit exponential, but not for K-S) – Severin Pappadeux Feb 17 '20 at 02:45

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