# Fit cdf and pdf from points on empirical cdf

I have cumulative counts with respect to a variable x, which looks like:

 x  cum_count
0        100
5        103
10        127
...       ...
Inf       187


From this, I want to arrive at an estimated pdf, maybe using kernel density estimation. How can it be done? Note that the Inf is actually present in the data.

• Is x continuous or discrete? Are the x-values in your data supposed to represent ranges (in the continuous case)? If the values are discrete, you need a pmf rather than a pdf. Also, if the values are discrete, will we always get integer multiples of 5 only?
– Carl
Apr 21, 2020 at 7:36
• Are the choices for the values of the points on the cumulative CDF exactly the same as the observed values? E.g.can we deduce that there are 3 values $x = 5$. Or are the points arbitrary, unrelated to the observed values, and should we deduce that there are 3 values with $0 < x \leq 5$? Dec 15, 2022 at 7:11

In my opinion you can:
 x  empirical CDF