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From this article, I read that the author drew four versions of CDFs each plotted in different distributions (all four plots come from the same sample data)

enter image description here

From these four plots, the author chooses specifically the Weibull distribution because the sample data is best represented in Weibull distribution. And he draws the following conclusion:

"A similar assessment can be made with a probability plot, which shows this is a predictable process and that 91 percent of the ER waiting times are within four hours."

enter image description here

Why did he specifically choose Weibull distribution to draw that conclusion? Couldn't you just use the CDF plotted in lognormal, exponential, or normal scale to draw the same conclusion?

My understanding of interpreting CDF says that reading percentiles should not be affected by different distribution scales.

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    $\begingroup$ I am assuming he chose Weibull because it has a non-significant and highest p-value of them all, based on a goodness of fit test. $\endgroup$ – user2974951 Feb 19 '19 at 8:40
  • $\begingroup$ @user2974951 Yes, but how does it affect reading the percentiles? Does the inverse of percentiles yield different values for different distributions? $\endgroup$ – Eric Kim Feb 19 '19 at 21:52
  • $\begingroup$ Could it be based on the Anderson-Darling statistic value? Lower the AD value, better the fit. $\endgroup$ – Saikiran Garimella Apr 15 '19 at 18:12
  • $\begingroup$ If you look closely at the large plot, you will notice that the calculation uses the fitted line rather than the data points. It should be clear that the lines in the small plots fit the data points rather differently, implying the answer depends on which plot is used. $\endgroup$ – whuber Apr 15 '19 at 20:19

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