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I have a discrete sample, numebr of passengers. when I try to find the best fit to this data set, none of the discrete distribution give the good fit according to goodness of fitness test. but the probability density function seems to be ok for example for Neg Binomial Should I rely on the plot or goodness of fitness test result? If I rely on GOF, all the distribution rejected. That means nothing fit to my data? I just want to use discrete distribution. and I have tried all the 8 famous discrete distributions.

Here is my number of passanger data:

 Passengers |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         18        6.19        6.19
          1 |         27        9.28       15.46
          2 |         37       12.71       28.18
          3 |         46       15.81       43.99
          4 |         37       12.71       56.70
          5 |         24        8.25       64.95
          6 |         40       13.75       78.69
          7 |         20        6.87       85.57
          8 |         10        3.44       89.00
          9 |         14        4.81       93.81
         10 |          4        1.37       95.19
         11 |          9        3.09       98.28
         12 |          4        1.37       99.66
         13 |          1        0.34      100.00
------------+-----------------------------------
      Total |        291      100.00
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  • $\begingroup$ The p values associated with goodness of fit tests, like all p-values, are partially a function of sample size. If you have a large sample, even very small deviations will be significant. $\endgroup$ – Peter Flom - Reinstate Monica Apr 8 '13 at 10:31
  • $\begingroup$ My sample size is 291. why always my critical value is less than t-statistic of GOF tests? $\endgroup$ – rose Apr 8 '13 at 10:36
  • $\begingroup$ To answer that, we'd need to see your data, perhaps in a table or a histogram. $\endgroup$ – Peter Flom - Reinstate Monica Apr 8 '13 at 10:37
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    $\begingroup$ Why do you want to fit a distribution in the first place? Doing that with these data will bring you little but grief, because it will obliterate some of the most salient features of these data, such as their bimodality. $\endgroup$ – whuber Apr 8 '13 at 17:32
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    $\begingroup$ So the purpose of this excercise is to create random samples which are similar to the observed data? In that case, would resampling from the data with replacement be a solution? That way you would just avoid the modeling problem. $\endgroup$ – Maarten Buis Apr 9 '13 at 13:13

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