Talk:Rademacher distribution

Inconsistent use of mode in table
In Bernoulli distribution the definition as on http://en.wikipedia.org/wiki/Mode_(statistics) is used (all the values with max probability mass are shown). Here it says NA, whereas the situation is identical. If someone can check my thinking on this, it can be fixed (don't want to fix it if I am overlooking something simple). Kasterma (talk) 12:34, 18 August 2014 (UTC)

Unclear section on bounds
A section added today entitled Bounds on sums says


 * Let x be a random variable with a Rademacher distribution. Let yi be a sequence of real numbers. Then


 * $$ P( \sum ( x y_i ) > t || y ||_2 ) \le e^{ \frac{ t^2 }{ 2 } } $$


 * where || ||2 is the quadratic norm and P(a) is the probability of event a.

I have various problems with this. First, on Wikipedia we denote random variables with capital letters (X instead of x). Second, t needs to be defined and given a range. Third, the summation is unclear: is the random variable X taking on various values xi (in which case it should be xi in the summation) so that we are simply taking a weighted sum of independently drawn values of X? Or is it something else? This needs to be clarified. Fourth, this inequality says that a probability is less than or equal to something that is always greater than 1, which is always true of probabilities and so provides no information about this particular distribution. Fifth, y is not defined -- is it supposed to be the vector with elements yi, so that ||y||2 is the square root of the sum of the squares of the yi? Sixth, while the section title mentions bounds on sums, this is apparently intended to be a bound on a probability.

Then the new section says


 * If ||yi||1 is finite then


 * $$ P( \sum ( x y_i ) > t || y ||_1 ) = 0 $$

The same questions apply to this, and also the norm ||.||1 needs to be explicitly defined.

Given that the new section is currently uninterpretable, I'm reverting it. I hope that it will be substantially clarified and reinserted. Duoduoduo (talk) 16:54, 14 May 2013 (UTC)