1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Variation distance?

  1. Jan 9, 2010 #1
    I was doing some reading and I came across this:


    So apparently for the finite case,

    [tex]\max_{x} ( \left| P(x) - Q(x) \right|)\quad \mbox{ is equivalent to}\quad \frac{1}{2} \sum_x {\left| P(x)-Q(x)\right|}[/tex]

    but isn't this is a counterexample?
    Code (Text):

    x         1        2        3        4
    P(x)    0.25     0.25     0.25      0.25

    Q(x)    0.10     0.20     0.35      0.35

    |P-Q|   0.15     0.05     0.10      0.10
    sum(|P-Q|)/2= 0.2


    So I was thinking, maybe they meant 'equivalent' in a different sense? Could somebody please explain?
  2. jcsd
  3. Jan 9, 2010 #2
    I believe they might mean that those two metrics define the same topology on the set of probability measures.
  4. Jan 10, 2010 #3


    User Avatar
    Science Advisor

    Rochfor1 is correct. "Equivalent" simply means that they will give the same results in any probability measures, not that they are equal.
  5. Jan 10, 2010 #4
    Thanks guys.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook