Rrerku

I am trying to find a suitable distribution to describe my data, and as one of the first few steps I created a Cullen and Frey Graph using the descdist command from the fitdistrplus package in GNU R:

library("fitdistrplus")
descdist(df$data, boot=1000)

The data describes the curvature on a point of a surface, with the different observations coming from equivalent points on different objects. Here is the plot for some point on the objects:

For most of the points on the surface, the plot looks very similar to the one shows above (note the bootstrapped points in yellow). However, for certain points it looks quite different, like this:

I would like to know how to interpret this pattern of the bootstrapped points. What does it tell me?

Visual inspection of the atypical points suggests they are in the area where the curvature is almost zero, in case that helps.

Here is my data (output of dput(df$data)) for the upper plot:

c(-0.00076386, 0.045336, 0.014051, -0.041787, 0.023339, 0.014239, 
0.0092057, 0.0084301, 0.020943, 0.01019, -0.0028119, -0.016991, 
-0.00098921, -0.033097, 0.0016237, 0.0012549, 0.0019851, 0.016966, 
-0.00068282, 0.0061208, 0.0029958, 0.018494, 0.00025555, -3.0299e-05, 
-0.00091132, 0.014321, 0.0073784, 0.01479, 0.023929, -0.0063367, 
0.0025699, 0.015087, 0.0014208, 0.001467, -0.00020386, 0.0037273, 
-0.014093, 0.0011921, -0.014109, 0.022459, 0.0078118, -0.00022082, 
0.0010377, 0.001418, 0.0010154, 0.0028933, 0.0019557, 0.0057984, 
-0.0008368, 0.0026886, -0.0050151, -0.0012167, 0.0030177, 0.010013, 
0.022312, -0.001848, -0.012818, -0.00043589, 0.0053455, 0.0032089, 
0.0032384, 0.011193, 0.017151, -0.0066761, -0.0025546, 0.01298, 
-0.0042231, 0.0024245, 0.0015398, 0.013608, 0.0039484, 0.00081566, 
0.01092, 0.011098, 0.0075705, 0.0038331, 0.014112, 6.1992e-05, 
0.003862, 0.0085052, 0.010609, -0.00041915, -0.0046417, -0.00064619, 
-0.032221, 0.0043921, 0.0028192, -0.00086485, -0.0062318, -0.011283, 
0.027339, 0.0033532, 0.011519, 0.0073512, -0.0017631, 0.0023497, 
0.0051281, 0.0046738, 0.0057097, -0.0011277, 0.11261, -0.0027572, 
0.0050015, 0.0089537, 2.4617e-07, 0.0025699, -0.0086815, -0.0050313, 
-0.033569, -0.0158, 0.0045544, 0.016692, 0.00051091, -0.013249, 
0.0030051, 0.0026081, 0.004686, 0.00019892, -0.0039485, -0.0079521, 
0.0012888, 0.012825, -0.0047024, -0.009024, 0.0023051, -0.0046861, 
0.0039009, -0.0024666, -0.00042277, -0.0023346, -0.0011262, 0.0013752, 
-1.813e-05, -0.011235, 0.00092171, 0.0025105, 0.0029965, 0.010461, 
0.0051702, -0.0021151, -0.015144, 0.00026214, 0.032263, 0.0077962, 
0.012388, -0.0034825, -0.014544, -0.0013833, -0.00096014, -0.0069078, 
-3.981e-05, 0.00030865, -0.014931, -1.7708e-05, -0.0061038, 0.0012174, 
-0.0024902, -0.0014924, 1.0677e-05, 0.00043018, 0.0050422, 0.021948, 
0.0097848, 0.0016898, -0.025803, 0.010538, 0.020389, 0.0071247, 
0.0089641, -0.0063912, 0.0029227, -0.023798, -0.005529, -0.01055, 
-0.00035134, -0.00039021, -0.010132, 0.0026251, 1.1334e-05, 0.0049617, 
-0.00043359, 0.015602, 0.0031481, 0.0011061, 0.033732, 0.03997, 
0.0037297, 0.025704, -0.0081762, 0.003853, 0.01115, 0.0033351, 
0.0035474, 0.0050837, 0.0055254, -0.012532, 0.0032077, 0.0012311, 
0.028543, -0.0077595, -0.017084, 0.0022539, 0.016777, -0.0045712, 
0.050084, 0.0015685, -0.011741, 0.0010876, 0.0106, -0.0033016, 
5.8685e-05, 0.007614, -0.012613, 0.010031, 0.0058827, 0.019654, 
0.0011954, 0.00053537, -0.0059612, 0.057128, 0.0035003, -0.0047389, 
0.010864, -0.0020918, 0.0034695, 0.0071228, -0.0094212, 0.01368, 
0.0031702, -0.003895, 0.0009593, -0.010492, 0.001612, 0.0032088, 
-0.0077312, 0.016688, 0.00012541, -0.0067579, -0.0054365, 0.0021638, 
0.0095235, 0.17428, 0.0084727, 0.010209, -0.020409, 0.022679, 
0.0095846, -0.00041361, 0.0059134, 0.0043463, -4.8011e-05, 0.0003717, 
-0.017807, -0.0085258, 0.013516, -0.011611, -0.0012556, 0.0057282, 
-0.00029204, 0.0040735, 0.0079601, 0.0029876, 0.14456, -3.5497e-05, 
-0.0016229, -0.00142, 0.0024437, -0.0019965, 0.0047731, -0.0069031, 
-0.0024837, -0.0063217, -0.0037023, -0.0011777, 0.014164, 0.032929, 
0.0012199, -0.006876, -0.0033327, -0.0049642, 0.00033994, -0.019737, 
-0.0006757, -0.010813, 0.0039238, -0.0033379, -0.01205, -0.014741, 
0.0008597, 0.00086404, 0.020482, -0.0071236, 0.0081256, 0.01513, 
-0.0052792, -0.017796, 3.7647e-05, -0.0011636, 0.0039913, 0.021583, 
-0.010653, -0.0020395, 0.011516, 0.0026764, 0.018921, 0.015807, 
-0.00035428, 0.0025714, 0.0074256, -0.0079076, 0.00064029, -0.001052, 
-0.0049469, 0.007442, -0.012999, 0.011805, 0.0020448, -9.4241e-05, 
-0.0035942, 0.010951, -0.0042067, -0.00011169, -0.0010933, -0.0042723, 
-6.3584e-05, -0.027255, 0.088819, 0.0018361, 0.013476, 0.0071269
)

And here for the lower:

c(-0.014512, -0.0058534, 0.0087152, -0.0078163, 0.056314, 0.029747, 
-0.052597, -0.012501, -0.0036789, -0.014999, -0.012793, -0.044215, 
-0.021863, 0.0087065, -0.011399, -0.019325, 0.013824, 0.0095986, 
-0.004078, -0.014264, -0.011927, 0.0011146, -0.0038653, 0.018538, 
-0.0041803, -0.0099991, -0.025937, 0.023628, -0.0075893, -0.0151, 
-0.0097623, -0.060885, 0.0074398, -0.023108, -0.02431, 0.059038, 
-3.2965e-06, 0.017071, 0.043786, -0.010216, -0.0066353, 0.0027318, 
-0.019151, 0.0047186, -0.051626, -0.00012959, -0.01279, -0.013684, 
0.00094597, 0.014003, 0.01486, -0.037267, -0.014702, -0.01956, 
-0.010359, -0.01508, -0.029832, -0.010463, -9.8748e-05, 0.0088553, 
-0.0025825, -0.04585, 0.0017103, 0.0010617, -0.014712, -0.058952, 
-0.018465, -0.0086677, -0.090302, -0.012687, 0.031989, -0.0010789, 
0.0011435, -0.0052397, -0.028672, -0.00047859, 0.0072699, 0.01623, 
-0.04801, -0.022326, -0.0015933, -0.038886, -0.025243, -0.0022138, 
0.0010459, -0.0057455, -0.019607, 0.0041099, -0.015831, -0.0012497, 
-0.14231, 0.0040444, 0.0073692, -0.0049665, 0.0095247, 0.035928, 
-0.026798, 0.0020477, 0.0020694, 0.0068247, -0.017784, -0.044672, 
-0.054571, -0.0030117, -0.031704, -0.0097623, -0.0066902, -0.075524, 
-0.0047395, -0.021042, 0.079442, 0.032306, 0.021644, -0.0014506, 
-0.011429, -0.038478, -0.010556, -0.014817, -0.0074413, 0.012451, 
-0.02684, 0.0054708, -0.02627, -0.024904, 0.011484, -0.0014307, 
-0.0028452, -0.03075, 0.00027497, -0.03346, 0.026292, 0.0030234, 
0.0058075, -0.019708, -0.012555, -0.016345, -0.03254, 0.034036, 
-0.046767, 0.0074342, -0.00068815, -0.014836, -0.024488, 0.0046096, 
-0.042042, -0.0046255, -0.021847, -0.0064215, 0.012622, -0.0026051, 
-0.057209, 0.038872, -0.016165, 0.015988, 0.016275, -0.016162, 
-0.015021, 0.020844, -0.014098, 0.0031134, 0.00099532, -0.017317, 
-0.063793, 0.0018859, 0.01971, -0.032403, -0.0024375, -0.00073467, 
-0.0074275, -0.00087284, 0.0083021, 0.014111, -0.018832, -0.00083409, 
0.00065538, -0.024792, -0.017424, 0.018622, -0.012342, -0.024214, 
-0.00038098, 0.0056994, -0.021689, -0.063995, 0.012623, -0.0038429, 
-0.078226, -0.01671, -0.0069796, -0.014817, -0.029802, 0.0042582, 
0.001967, 0.0011492, -0.0015149, 0.0071541, -0.014131, -0.042844, 
-0.019941, -0.02201, -0.0035923, -0.012501, 0.00031213, -0.0012541, 
-0.0075098, -0.047008, -0.026675, -0.021419, -0.010504, 0.0018293, 
-0.032401, 0.011153, -0.00094015, -0.031386, -0.031001, 0.0019511, 
-0.012967, -0.012911, 0.0074449, 0.0052992, 0.069074, -0.022406, 
-0.0028998, -0.0037614, 0.019345, -0.032463, -0.030929, 0.0098452, 
-0.01751, -0.018875, -0.015721, -0.003342, -0.01194, -0.005254, 
-0.054454, 0.073446, 2.9542e-05, -0.060855, 0.01012, -0.049511, 
-0.01284, -0.014399, 0.019037, -0.03636, -0.034068, -0.012705, 
-0.03571, -0.018263, -0.0059382, -0.022954, 0.013382, -0.095539, 
0.0086911, -0.038144, 0.074835, -0.019483, -0.032716, -0.0025377, 
-0.0099221, -0.0057603, 0.018333, 1.3211, 0.020368, 0.041849, 
-0.064433, 0.0017635, 0.023663, -0.0012425, -0.13279, 0.017999, 
0.031229, 0.058787, -0.037184, -0.016621, 0.011081, 0.011349, 
0.0026947, 0.019077, 0.0051954, -0.036936, 0.0045157, -0.023299, 
-0.054993, -0.031168, -0.06061, -0.0086002, -0.045094, -0.019699, 
-0.0025394, 0.021987, -0.05349, -0.008101, -0.0074635, -0.010358, 
-0.068063, 0.013118, 0.013409, -0.018069, 0.0015969, -0.00024499, 
0.016927, -0.011481, -0.0053067, 0.0024216, 0.012565, -0.0011296, 
0.017863, -0.073312, 0.092955, -0.034487, -0.031434, -0.007217, 
-0.038946, -0.0070417, -0.11002, 0.069496, -0.0079777, -0.050645, 
-0.0062267, 0.070627, 0.044814, -0.0028551, -0.013993, -0.0094418, 
0.037753, -0.0071857, -0.014971, -0.0021806, -0.046116, -0.00089069
)

[My previous answer had a fatal mistake in it, so I deleted it and made a new one.]

Here's a more basic plot instead of your fancy plot. The black line is the density plot your first dataset, and the red line is of your second. (Note that the first dataset is more compact, so its density goes off the top.)

You see at least 4 discretized points in your first dataset, which density has turned into humps. You see an odd hump in your second dataset near the first dataset's four -- which might be a truncation of similar values -- and then a bump way out on the right and a bump to the left.

Do you know how your data is captured? For example, are you scanning objects with software that places points farther apart in areas of low curvature? (This might be the result if your objects are captured as quadrangles, with adjacent quadrangles that have a low angle between them joined into a single quadrangle? Or it might be that your capture process is driven by changes in reflectivity -- i.e. curvature -- that must exceed a threshold before a data point is recorded?)

My guess as to your original strange graph for your second dataset is that the bump way out on the right caused things to scale oddly, so you got a discretized graph.

Your raw data appears to be a mixture of data generation processes and data capture artifacts (which might include truncation, censoring, discretization, and noise). So the question is: do you want a single distribution for all of your data as captured, or for your data after accounting for artifacts, or something else?

Trying to come up with a single distribution for a mixture of process results is usually a bad idea.