Tell me more ×
Cross Validated is a question and answer site for statisticians, data analysts, data miners and data visualization experts. It's 100% free, no registration required.
up vote 7 down vote favorite
2

How can I find the PDF (probability density function) of a distribution given the CDF (cumulative distribution function)?

share|improve this question
4  
I am not sure I understand the difficulty. If the functional form is known just take the derivative otherwise take differences. Am I missing something here? – user28 Jul 19 '10 at 19:31

2 Answers

up vote 7 down vote accepted

As user28 said in comments above, the pdf is the first derivative of the cdf for a continuous random variable, and the difference for a discrete random variable.

In the continuous case, wherever the cdf has a discontinuity the pdf has an atom. Dirac delta "functions" can be used to represent these atoms.

share|improve this answer
up vote 3 down vote

For a continuous random variable you can always approximate the pdf by calculating (CDF(x2) - CDF(x1))/(x2 - x1) where x1 and x2 are on either side of the point where you want to know the pdf and the distance |x2 - x1| is small.

share|improve this answer
Thats the same as taking the derivative, but just more inaccurate so why would you do it? – Matti Pastell Jul 20 '10 at 9:39
2  
This would be the approach when the CDF is only approximated empirically. It gives lousy estimates of the PDF, though. – shabbychef Oct 20 '10 at 5:13

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.