I was playing with R, I started with adding consecutive binomials (the n parameter of the second binomial variable depends of the result of the first binomial and so on...). After a few more operations I got this histogram. I was trying to model something.

This is just me having "fun". After a few frustrating attempts, I gave up on deriving a theoretical distribution for it.

I decided to simply pick a distribution have a fit, and see if I can justify. But even for this I am stuck! I tried a few, but none of them seem to have the right combination of skewness, mean and variance.

To sum up, the question is simple, do you know any probability distribution shaped like this (continuous or discrete)? (this histogram is for a discrete distribution, the frequencies before 3 are 0, and 7 gave me 1))

enter image description here

  • $\begingroup$ What about using a multinomial? $\endgroup$ Nov 19 '20 at 20:13
  • $\begingroup$ Thank you! I am still new to probilitites and stats and I did not think of this one. Not only that but it makes sense in my model as I can attempt to derive the probabilities of the categories. $\endgroup$ Nov 19 '20 at 20:50
  • $\begingroup$ @javierazcoiti Multinomial works! Thank you $\endgroup$ Nov 19 '20 at 20:51
  • $\begingroup$ Can you describe the operations tours performing in the first paragraph in more detail? It might be possible to derive a distribution (either exact or approximate) $\endgroup$
    – Glen_b
    Nov 20 '20 at 2:43
  • $\begingroup$ You really needs to give the details (code pr formulas) of what you did ... $\endgroup$ Nov 20 '20 at 16:30

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