Obtaining a normalized PDF from a histogram?

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To obtain a normalized probability density function (PDF) from a histogram, one must divide the frequency counts by the total number of counts, resulting in an approximation of the underlying PDF. To derive an explicit form for the PDF, curve fitting techniques can be employed. If the distribution type is known (such as binomial or normal), the mean and variance should be estimated and used to define the specific parameters. In cases where the distribution is unknown, a general curve fitting approach should be applied, ensuring that the integral of the fitted curve equals one. This process effectively transforms the normalized histogram into a usable PDF.
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Suppose I have a regular histogram, I can normalize it by dividing the frequency counts by the total number of counts (at least I believe that's all you need to do).

What you're left with should be an approximation to the underlying PDF (probability density function). What I'm asking is how does one obtain an explicit form for the PDF from your normalized histogram?
 
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Essentially it is a curve fitting problem. If you know the type of distribution (e.g. binomial, Poisson, normal, etc.), estimate the mean and variance from the data and use the type with specific parameters. Otherwise, fit a curve and make sure the integral of the fit = 1.
 

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