1

I am currently having a read through the Statistical Drake Equation; a method of taking the Drake Equation, letting each number be a uniform random variable, and then applying the Central Limit Theorem to get the combined distribution of these variables.

But, as there are only 7 variables in this equation, why is it valid to say it tends to a Normal Distribution? Surely this isn't true as the number of variables definitely isn't large.

Shivam Malhotra
  • 57
  • 4
  • 1
    The CLT says absolutely nothing about the sum of seven variables, uniform or otherwise. However, sums of independent variables are well known. One could appeal to this theory to justify approximating the sum with a Normal distribution. Indeed, the last figure in my answer at http://stats.stackexchange.com/a/43075/919 illustrates the PDF for the sum of eight independent uniform variates. The answer itself provides various ways to characterize these sums, if you wish to compare them further to Normal distributions. – whuber Jun 09 '16 at 14:57
  • 1
    Please quote/describe the essential parts of the link and give a proper reference, and if possible explain the justification for the use of uniforms. – Glen_b Jun 09 '16 at 19:52
  • Or you can use a saddlepoint approximation, see https://stats.stackexchange.com/questions/191492/how-does-saddlepoint-approximation-work/191781#191781 – kjetil b halvorsen Sep 25 '17 at 07:49

0 Answers0