User talk:Lothar.brendel
Florian's eCDF
Good to know that "empirical probability" is a synonym for the relative frequency.
My own idea behind all this seemed way simpler to me at the time; although, I am not sure how to properly show that it does what it should at the moment. Basically, I conveniently forgot that the agglomerate sizes are restricted to natural numbers. From there, I can estimate the probability **density** by estimating the derivative of the CDF, in my case as discretized derivatives using the eCDF. However, this means that the values I calculated are estimates of the PDF, not of the probabilities as I originally wanted.
--Florian (talk) 14:54, 10 July 2024 (CEST)
By this logic, I am quite confused, because the PDF estimates are normalized to one. I would have expected that I need an integral for the normalization if I assumed continuous random numbers in the beginning.
--Florian (talk) 15:03, 10 July 2024 (CEST)
- When dropping \(n\in\mathbb N\), to which values \(n\) do you assign ficticious probabability(-density)-values and why? --Lothar (talk) 15:51, 10 July 2024 (CEST)
- \(p_{n_i} = \frac{c(n_i) - c(n_{i-1})}{n_i - n_{i-1}}\) is the assignment. There is actually no particular reason I chose this. In the picture of continuous random variables, any discretized derivative should, ignoring the discretization error, work just fine and should converge to the actual PDF for an infinitely large sample. If this is true for discrete random variables as well (i.e. that it converges to the correct probabilities), I do not know. --Florian (talk) 16:47, 10 July 2024 (CEST)