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probability or statistics - Why the results of FindDistribution and DistributionFitTest are not consistent? 


data = {0.180723, 0.181208, 0.182213, 0.1875, 0.1875, 0.1875, 0.1875,
0.1875, 0.1875, 0.190476, 0.191041, 0.19174, 0.192308, 0.192513
0.193038, 0.194118, 0.194858, 0.195172, 0.196141, 0.196507, 0.196911,

0.19717, 0.199725, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.2,
0.204804, 0.204887, 0.206148, 0.207435, 0.208861, 0.211034, 0.213389,
0.214286, 0.214286, 0.214286, 0.215247, 0.218447, 0.22028, 0.221334,
0.221519, 0.222222, 0.224227, 0.224359, 0.225352, 0.226485, 0.230769,
0.230769, 0.230769, 0.230769, 0.230769, 0.230769, 0.231561, 0.23622,
0.239075, 0.24, 0.24, 0.241667, 0.241758, 0.246269, 0.247842, 0.25,
0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.254902,
0.26087, 0.26087, 0.264706, 0.269461, 0.272727, 0.273684, 0.277778,
0.287576, 0.28934, 0.295775, 0.298013, 0.3, 0.3, 0.3, 0.3, 0.304124,
0.305085, 0.310345, 0.333333, 0.333333, 0.333333, 0.333333, 0.333333,

0.333333, 0.333333, 0.333333, 0.333333, 0.333333, 0.333333, 0.357143,
0.36, 0.375, 0.375, 0.375, 0.375, 0.375, 0.387097, 0.4, 0.409091,
0.409091, 0.5, 0.5, 0.6}

dataDist = FindDistribution[data,3,
   {"CramerVonMises","PearsonChiSquare"},"RandomSeed"->23544325]


{{GammaDistribution[7.34584,0.0353382],{0.896823,0.943734}}, {LogNormalDistribution[-1.41827,0.377612],{0.547505,0.252689}}, {WeibullDistribution[1.81133,0.194603,0.086273],{0.657403,0.786422}}}




Hdata=DistributionFitTest[data,GammaDistribution[7.34584,0.0353382],"HypothesisTestData"]


  Statistic   P-Value
Anderson-Darling    6.04043 0.000934535
Cramér-von Mises    0.923269    0.00372792
Pearson \[Chi]^2    77.2131 3.67716*10^-11

Based on the FindDistribution results the Gamma distribution seems to fit better these data.However, the DistributionFitTest did not confirm this conclusion. Why ? Where I am going the wrong way ?


Addendum:



The FindDistribution function does not handle these data set either:


data1={1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.,1.16667,1.33333,1.33333,1.33333,1.33333,1.33333,1.33333,1.33333,1.33333,1.33333,1.33333,1.33333,1.33333,1.33333,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.5,1.6,1.6,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.66667,1.73333,1.73333,1.73333,1.73333,1.73333,1.73333,1.8,1.8,1.8,1.8,1.8,1.86667,1.86667,1.86667,1.92857,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,1.93333,2.,2.06667,2.07143,2.07143,2.13333,2.13333,2.13333,2.13333,2.13333,2.13333,2.13333,2.13333,2.13333,2.13333,2.13333,2.13333,2.14286,2.14286,2.14286,2.19048,2.25,2.25,2.25,2.25,2.25,2.27778,2.28571,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.32143,2.33333,2.35714,2.4,2.5,2.51515,2.57778,2.57778,2.62121,2.64444,2.64444,2.64444,2.66667,2.68889,2.68889,2.68889,2.68889,2.68889,2.68889,2.68889,2.68889,2.68889,2.69091,2.71795,2.84848,2.87879,2.89394,2.98095,3.01515,3.01515,3.02857,3.06061,3.06061,3.15385,3.16484,3.16484,3.19697,3.24242,3.26374,3.27473,3.27473,3.44167,3.45833,3.48366,3.5,3.6,3.66667,3.97044,4.00833,4.07792,4.14667,4.22105,4.61846,6.35829,18.603,18.9127,20.0815,21.4653,21.8075,23.1257,23.174,23.195,24.8591,25.5128,25.6204,25.7491,27.2341,28.6521,29.1464,29.2351,29.9114,30.1133,30.7835,31.6615,32.4578,32.6746,34.5677,34.9822,35.3298,35.3304,35.5266,36.5512,36.9395,38.5341,38.5421,39.0514,44.5931,47.1162,63.3183,64.7268,72.3538,80.9747,87.87,90.8965}

    FindDistribution[data1, 3, {"CramerVonMises", "PearsonChiSquare"}, 
     "RandomSeed" -> 23544325]
{{MixtureDistribution[{0.950331, 
    0.0496689}, {LogNormalDistribution[0.354894, 0.349561], 
    LogNormalDistribution[3.62601, 0.392707]}], {0.0000939677, 
   1.61301*10^-90}}, {MixtureDistribution[{0.9503, 
    0.0496998}, {LogNormalDistribution[0.354858, 0.349509], 

    GammaDistribution[5.66106, 7.257]}], {0.0000935481, 
   1.61301*10^-90}}, {MixtureDistribution[{0.936836, 
    0.0631641}, {NormalDistribution[1.48875, 0.529605], 
    NormalDistribution[33.145, 23.7551]}], {0.0000256599, 
   1.04431*10^-135}}}

How can I make FindDistribution perform better in this case?


NB: This is an experimental data and it is what it is.




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