Obtaining a normalized PDF from a histogram?

[dipole]

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?

 

[mathman]

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.