I was doing some reading and I came across this:(adsbygoogle = window.adsbygoogle || []).push({});

http://en.wikipedia.org/wiki/Total_variation_distance_of_probability_measures

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?

sum(|P-Q|)/2= 0.2Code (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

max(|P-Q|)=0.15

So I was thinking, maybe they meant 'equivalent' in a different sense? Could somebody please explain?

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Variation distance?

Loading...

Similar Threads - Variation distance | Date |
---|---|

B Using trig to find distance? | Jan 18, 2018 |

I Question on Calculus of variations formalism | May 29, 2016 |

I Calculus of Variations Dependent variables and constraints | Apr 20, 2016 |

Permutation with exception/repetition | Dec 3, 2015 |

Graphing a variation of y=sin-x | Aug 5, 2015 |

**Physics Forums - The Fusion of Science and Community**