How do you fit/estimate a probability distribution using only the information from boxplot, i.e, max, min, 1st quartile, 3rd quartile and median? I don't have access to raw data but only a boxplot information is given.

  • $\begingroup$ Can't be done, although you might try to create some sort of empirical density function based on that data. $\endgroup$ Sep 12, 2018 at 13:06
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    $\begingroup$ do you have any other information that would allow you to hypothesise what the expected distribution would be? $\endgroup$
    – ReneBt
    Sep 12, 2018 at 13:26
  • $\begingroup$ @ReneBt, the only information given are the boxplot values, we don't have access to the raw data/values, but we know that the observations are discrete. $\endgroup$
    – bninopaul
    Sep 12, 2018 at 14:09
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    $\begingroup$ What can our cannot be advised depends on what you are doing with it and what exactly you know and how confident you need to be in the outcome. As @user2974951 says you can't create a distribution based on what you have told us. is this a study question and therefore you expect there to be a solution? If so you need to share the full context. Or is this something that you have no idea should work? $\endgroup$
    – ReneBt
    Sep 12, 2018 at 18:46
  • $\begingroup$ You need to be more specific about the source of the boxplots and your objectives. Perhaps looking at this somewhat similar Q & A will help you formulate a more specific question. // Do you anticipate the distributions may be normal and just need to find $\mu$ and $\sigma?$ Or do you have no clue about the data? History test scores? Times to failure of electronic devices? Liver enzyme data on hepatitis patients? // If you knew exact answer, how would you use that? $\endgroup$
    – BruceET
    Sep 12, 2018 at 22:16


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