3 ms·

Too cryptic to be helpful, sorry..

• srean 10y ago
  Ah I see, my apologies, I assumed Googling those keywords would be sufficient to connect the dots. The main thing that I wanted to convey is that the consequences of CLT does not come for free. It is not remotely as widely applicable as it is made out to be. CLT is also not so narrow that you need IID random variables as is often claimed. Those assumptions can be relaxed substantially. What gets in the way in obtaining a Gaussian distribution in the limit is the requirement that the original distribution(s) have a finite variance. The (averaging) process may still converge to some limiting distribution but it would not be a Gaussian one. Levy measures, more precisely stable measures are that class and Gaussian is but one member of that class, the only one that has finite variance. It is slowly getting acknowledged that many natural processes in fact do not have a finite variance. Fractals are one such process
  • platz 10y ago
    I wasn't aware of the idea that natural processes might not have a finite variance, or what implications that would have. Thanks for clarifying!
  • willhslade 10y ago
    I've seen variations of this comment in multiple threads, and have to ask: is there a good paper or textbook that spells this out?
    • srean 10y ago
      I would say go with books on (i) heavy tailed distributions and another on (ii) stable distributions. Communities that have quickly wizened up to the deficiencies of the Gaussian assumption are (a) mathematical finance (b) statistical analysis of network packets. Following that literature might also be useful.