0

I would like to get the probability distribution (either pdf or cdf) for a variable, by knowing the first n-moments of the distribution. I ask:

  • Is there a standard way to deal with this, and maybe a python package?
  • It is a matter of inverting the moment generating function or the characteristic function, that are expressed as series of moments. Is it legit to truncate these series to the first n-moments? When yes and when not?
  • What if I don't know the exact moments, but I rather estimate them from data? Does the inversion process above work well with noisy data?
kjetil b halvorsen
  • 63,378
  • 26
  • 142
  • 467
Marco Mene
  • 151
  • 5
  • 2
    You can't always do this; even all (infinite) moments aren't sufficient to identify a unique probability distribution. To put it another way, you can construct two different probability distributions that have the same moments of all orders. If you put other constraints on the distribution, though, then (depending on the constraints) you may be able to. – jbowman Sep 29 '17 at 13:53
  • 1
    Perhaps this thread has answered your questions? https://stats.stackexchange.com/questions/3390 – whuber Sep 29 '17 at 15:04

0 Answers0