0
$\begingroup$

Edwin Jaynes wrote in his book 'Probability Theory' that:

[it] is abnormal in the sense that it has many unique properties not possessed by any other.

(p.729). What could he mean by saying this? The book doesn't elaborate on this further.

Like sum of two other distributions is usually beyond of the family of summands' distribution? Or is it about three sigma rule? Or... ?

$\endgroup$
3
  • 2
    $\begingroup$ A play of words. Consider normal versus abnormal, and normal versus special. $\endgroup$
    – Gyro Gearloose
    Commented Dec 31, 2017 at 13:10
  • $\begingroup$ And that's it? Nothing more? $\endgroup$
    – Lil'Lobster
    Commented Dec 31, 2017 at 13:11
  • $\begingroup$ He was trying to be funny (i.e. "abnormal", following his own logic). $\endgroup$
    – user436658
    Commented Dec 31, 2017 at 13:34

1 Answer 1

Reset to default
3
$\begingroup$

Here are some properties the normal distribution possesses which aren't true in general:

  1. The sum of normal distributions is normal.
  2. The normal distribution is symmetric about its mean.
  3. The mean, median, and mode of the normal distribution agree.
  4. The normal distribution decays rapidly (faster than exponential).

Etc. etc. So all the author's saying is that there are many properties like this, making the normal distribution very special and not "normal," among distributions, at all.

(The sense in which the normal distribution has anything to do with "normality" is the central limit theorem: it's what "normally" happens when you add up a bunch of independent copies of a random variable.)

$\endgroup$

You must log in to answer this question.

Not the answer you're looking for? Browse other questions tagged .