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This question is derived from this one, which is related to empirical distribution.

I did a little bit search and then got this and this, unfortunately, none of them mentions "histogram".

I've searched the keyword "empirical distribution histogram" through all sites and got only one result that mentions the term without any explanation.

So, could someone give an concrete example to illustrate how "empirical distribution" relates to "histogram"?

Please give some concrete examples, such as Bernoulli distributions, normal distributions.

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Some -- indeed many -- histograms relate to theoretical distributions. They're an entirely natural and conventional way for showing theoretical discrete distributions in particular, such as binomial or Poisson distributions. (But how well they do that is an interesting and sometimes important detail, yet is another story.) With theoretical include fitted, predicted or simulated distributions.

The words empirical distribution histogram I would explain as follows, even confidently without seeing any instances of quotations.

First, and trivially, distribution is redundant. All histograms show distributions. That's their job. I suppose in some instances people might want to insist that they are showing a distribution in a histogram, not something else in a bar chart. (To statistical people, a histogram is not a bar chart, itself yet another tiny story.)

Second, empirical just means based on observed data. Depending on context, that might be redundant too, or it might be helpful in contrast with, as said, a histogram of theoretical or predicted or fitted or simulated distributions.

Similarly with any plot: an empirical scatter plot is not a different kind of scatter plot. The writer or presenter is just flagging that it is based on data.

Yet again, I quite often see the term empirical cumulative distribution plot where empirical is sometimes helpful emphasis and sometimes unnecessary. (Cumulative can be omitted for some readerships.) But you can't understand ECDF plot easily (jargon popular in some fields) if no-one explains all the words behind it.

(I am all for concrete examples in most questions but in this one I think all that is needed is a dictionary-type explanation such as I am trying to provide.)

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  • $\begingroup$ Thanks for your answer. Would you please give some concrete examples, such as Bernoulli distributions, normal distributions? $\endgroup$ – whnlp Sep 19 '19 at 5:00
  • $\begingroup$ I can't show empirical examples of normal distributions because they don't occur in nature. Bernoulli example: imagine that in my country there are so many sensible politicians and so many stupid politicians. Count the sensible and the stupid and their two frequencies could be shown on a histogram. $\endgroup$ – Nick Cox Sep 19 '19 at 7:17

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