Obtaining a normalized PDF from a histogram?

In summary, to normalize a regular histogram, divide the frequency counts by the total number of counts. This results in an approximation of the underlying probability density function (PDF). To obtain the explicit form of the PDF, you can either use a known distribution and estimate the parameters, or fit a curve and ensure the integral equals 1.
  • #1
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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  • #2
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.
 

1. What is a normalized PDF?

A normalized PDF (Probability Density Function) is a mathematical function that describes the relative likelihood of observing a particular value in a given dataset. It is normalized to have an area of 1, making it a probability distribution.

2. Why is it important to obtain a normalized PDF from a histogram?

Obtaining a normalized PDF from a histogram allows for easier comparison between different datasets, as it removes the influence of the data's scale and size. It also allows for easier interpretation of the data's distribution and probabilities.

3. How do you obtain a normalized PDF from a histogram?

To obtain a normalized PDF from a histogram, you must divide each bin's frequency by the total number of observations and then divide by the bin's width. This will result in a PDF that is normalized to have an area of 1.

4. What are some common methods for smoothing a histogram before obtaining a normalized PDF?

Some common methods for smoothing a histogram include using a moving average, kernel density estimation, or Gaussian smoothing. These methods can help to reduce the impact of outliers and noise in the data.

5. Can a histogram with a small number of bins accurately represent a dataset's distribution?

No, a histogram with a small number of bins may not accurately represent a dataset's distribution as it can result in oversimplification and loss of important information. It is recommended to use a sufficient number of bins to accurately depict the data's distribution.

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