Obtaining a normalized PDF from a histogram?

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SUMMARY

To obtain a normalized Probability Density Function (PDF) from a histogram, one must divide the frequency counts by the total number of counts. This process yields an approximation of the underlying PDF. For explicit PDF forms, curve fitting techniques are employed, particularly when the distribution type is known (e.g., binomial, Poisson, normal). Estimating parameters such as mean and variance is crucial, and the fitted curve must satisfy the condition that its integral equals 1.

PREREQUISITES
  • Understanding of histogram normalization techniques
  • Familiarity with probability distributions (e.g., binomial, Poisson, normal)
  • Knowledge of curve fitting methods
  • Basic calculus for integration of functions
NEXT STEPS
  • Research curve fitting techniques using tools like SciPy in Python
  • Learn about parameter estimation for different probability distributions
  • Explore normalization methods for histograms in data analysis
  • Study the properties of probability density functions and their integrals
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Data analysts, statisticians, and researchers involved in statistical modeling and data visualization will benefit from this discussion.

dipole
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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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