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Suppose, I have a histogram (or a "discrete" frequency counter):

X = {0.1: 3, 0.2: 5, 0.41: 1, 0.45: 5, 0.5: 3, 0.7: 9}

What is the best possible way to convert it to a continuous function, so that, one can query the "frequency" for any number? I was reading on KDE but not able to get my head around it.

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    $\begingroup$ If you have 3 values at exactly 0.1 then your values are discrete, not continuous, so it's unclear what you mean by "convert". Are your values rounded or binned in some fashion? $\endgroup$
    – Glen_b
    Dec 27, 2017 at 4:11
  • $\begingroup$ +1 to what @Glen_b said. If your data are truly continuous, you may also consider density smoothing, see here: en.wikipedia.org/wiki/Density_estimation which will allow you to query the density (which is a different quantity from the frequency) $\endgroup$
    – Jeremias K
    Dec 27, 2017 at 13:12

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From what you wrote, I gather two things. First there are 26 observations. Secondly, the data does not have a smooth shape: clear symmetry or asymmetry.

Your question may need more information for a proper answer, if there's theoretical support for it (in the literature), you can use some specific parametric distribution. Nonparametric estimators do exist but they may not be all that reliable with only 26 observations.

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